Bibliography Bibliography D Bibliography F

Bibliography E

♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

J. Écalle (1981a) Les fonctions résurgentes. Tome I. Université de Paris-Sud Département de Mathématique, Orsay (French).
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External Links:

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Referenced by:

§2.7(ii).

Encodings:

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J. Écalle (1981b) Les fonctions résurgentes. Tome II. Université de Paris-Sud Département de Mathématique, Orsay (French).
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External Links:

MathReview (Carlos A. Berenstein)

Referenced by:

§2.7(ii).

Encodings:

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C. Eckart (1930) The penetration of a potential barrier by electrons. Phys. Rev. 35 (11), pp. 1303–1309.
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External Links:

Document, ZentralBlatt

Referenced by:

§15.18.

Encodings:

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U. Eckhardt (1980) Algorithm 549: Weierstrass’ elliptic functions. ACM Trans. Math. Software 6 (1), pp. 112–120.
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Notes:

Single-precision Fortran, maximum accuracy 18D.

External Links:

ISSN 0098-3500, Document, GAMS (module 549; package TOMS)

Referenced by:

1st item.

Encodings:

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ECMNET Project (website)
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Notes:

Links to software for elliptic curve methods of factorization and primality testing.

External Links:

Home Page

Referenced by:

4th item.

Encodings:

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A. R. Edmonds (1974) Angular Momentum in Quantum Mechanics. 3rd printing, with corrections, 2nd edition, Princeton University Press, Princeton, NJ.
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Notes:

Reprinted in 1996.

External Links:

ISBN 0-691-02589-4, MathReview, ZentralBlatt

Referenced by:

§14.30(i), §14.30(ii), §14.30(iii), §14.30(iv), §14.30(iv), §14.31(iii), (34.1.1), §34.1, §34.1, §34.13, §34.2, §34.3(i), §34.3(i), §34.3(ii), §34.3(iii), §34.3(iv), §34.3(vii), §34.3(vii), §34.4, §34.5(i), §34.5(ii), §34.5(iii), §34.5(iv), §34.5(vi), §34.6, §34.7(i), §34.7(ii), §34.7(iv), §34.7(vi), Ch.34, Erratum (V1.0.14) for Section 34.1, Erratum (V1.0.15) for Section 34.1.

Encodings:

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H. M. Edwards (1974) Riemann’s Zeta Function. Academic Press, New York-London.
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Notes:

Pure and Applied Mathematics, Vol. 58. Reprinted by Dover Publications Inc., Mineola, NY, 2001.

External Links:

MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

Ch.25.

Encodings:

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J. Edwards (1954) A Treatise on the Integral Calculus. Vol. 1-2, Chelsea Publishing Co., New York.
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Notes:

Originally published by Macmillan, 1921-1930.

External Links:

ZentralBlatt

Referenced by:

§19.11(i), §19.4(ii).

Encodings:

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M. Edwards, D. A. Griggs, P. L. Holman, C. W. Clark, S. L. Rolston, and W. D. Phillips (1999) Properties of a Raman atom-laser output coupler. J. Phys. B 32 (12), pp. 2935–2950.
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External Links:

FullText

Referenced by:

§12.17.

Encodings:

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G. P. Egorychev (1984) Integral Representation and the Computation of Combinatorial Sums. Translations of Mathematical Monographs, Vol. 59, American Mathematical Society, Providence, RI.
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Notes:

Translated from the Russian by H. H. McFadden, Translation edited by Lev J. Leifman

External Links:

ISBN 0-8218-4512-8, MathReview, ZentralBlatt

Referenced by:

§15.17(iv).

Encodings:

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U. T. Ehrenmark (1995) The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature. J. Comput. Appl. Math. 61 (1), pp. 43–72.
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External Links:

ISSN 0377-0427, Document, MathReview (J. P. Singhal), ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

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M. Eichler and D. Zagier (1982) On the zeros of the Weierstrass $\wp$ -function. Math. Ann. 258 (4), pp. 399–407.
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External Links:

ISSN 0025-5831, Document, MathReview (Toyokazu Hiramatsu), ZentralBlatt

Referenced by:

§23.13.

Encodings:

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Á. Elbert (2001) Some recent results on the zeros of Bessel functions and orthogonal polynomials. J. Comput. Appl. Math. 133 (1-2), pp. 65–83.
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External Links:

ISSN 0377-0427, Document, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§10.21(iv).

Encodings:

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Á. Elbert and A. Laforgia (1994) Interlacing properties of the zeros of Bessel functions. Atti Sem. Mat. Fis. Univ. Modena XLII (2), pp. 525–529.
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External Links:

ISSN 0041-8986, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§10.21(i).

Encodings:

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Á. Elbert and A. Laforgia (1997) An upper bound for the zeros of the derivative of Bessel functions. Rend. Circ. Mat. Palermo (2) 46 (1), pp. 123–130.
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External Links:

ISSN 0009-725X, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.21(vii).

Encodings:

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Á. Elbert and A. Laforgia (2000) Further results on McMahon’s asymptotic approximations. J. Phys. A 33 (36), pp. 6333–6341.
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External Links:

ISSN 0305-4470, Document, MathReview (R. G. Aĭrapetyan), ZentralBlatt

Referenced by:

§10.21(vi).

Encodings:

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Á. Elbert and A. Laforgia (2008) The zeros of the complementary error function. Numer. Algorithms 49 (1-4), pp. 153–157.
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External Links:

ISSN 1017-1398, Document, FullText, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§7.13(ii).

Encodings:

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E. Elizalde (1986) An asymptotic expansion for the first derivative of the generalized Riemann zeta function. Math. Comp. 47 (175), pp. 347–350.
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External Links:

ISSN 0025-5718, FullText, MathReview (S. Audinarayana Moorthy), ZentralBlatt

Referenced by:

(25.11.44), (25.11.45), §25.11(xii), §25.11(xii).

Encodings:

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E. Elizalde (1995) Ten Physical Applications of Spectral Zeta Functions. Lecture Notes in Physics. New Series m: Monographs, Vol. 35, Springer-Verlag, Berlin.
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External Links:

ISBN 3-540-60230-5, MathReview (Alfred Actor), ZentralBlatt

Referenced by:

§25.17.

Encodings:

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D. Elliott (1971) Uniform asymptotic expansions of the Jacobi polynomials and an associated function. Math. Comp. 25 (114), pp. 309–315.
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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§18.15(i).

Encodings:

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D. Elliott (1998) The Euler-Maclaurin formula revisited. J. Austral. Math. Soc. Ser. B 40 (E), pp. E27–E76 (electronic).
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External Links:

ISSN 0334-2700, FullText, MathReview (J. Németh), ZentralBlatt

Referenced by:

§2.10(i).

Encodings:

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E. B. Elliott (1903) A formula including Legendre’s $EK^{\prime}+KE^{\prime}-KK^{\prime}=\frac{1}{2}\pi$ . Messenger of Math. 33, pp. 31–32.
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Notes:

Errata on p. 45 of the same volume.

External Links:

ZentralBlatt

Referenced by:

§15.16.

Encodings:

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W. J. Ellison (1971) Waring’s problem. Amer. Math. Monthly 78 (1), pp. 10–36.
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External Links:

Document, FullText, MathReview (J. W. S. Cassels), ZentralBlatt

Referenced by:

§27.13(iii), §27.13(iii).

Encodings:

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S. P. EraŠevskaja, E. A. Ivanov, A. A. Pal’cev, and N. D. Sokolova (1973) Tablicy sferoidal’nyh volnovyh funkcii i ih pervyh proizvodnyh. Tom I. Izdat. “Nauka i Tehnika”, Minsk (Russian).
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Notes:

Translated title: Tables of Spheroidal Wave Functions and Their First Derivatives.

External Links:

MathReview, ZentralBlatt

Referenced by:

4th item.

Encodings:

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S. P. EraŠevskaja, E. A. Ivanov, A. A. Pal’cev, and N. D. Sokolova (1976) Tablicy sferoidal’nyh volnovyh funkcii iih pervyh proizvodnyh. Tom II. Izdat. “Nauka i Tehnika”, Minsk (Russian).
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Notes:

Edited by V. I. Krylov. Translated title: Tables of Spheroidal Wave Functions and Their First Derivatives.

External Links:

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Referenced by:

4th item.

Encodings:

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N. Ercolani and A. Sinha (1989) Monopoles and Baker functions. Comm. Math. Phys. 125 (3), pp. 385–416.
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External Links:

ISSN 0010-3616, Link, MathReview (Jacques Hurtubise), ZentralBlatt

Referenced by:

§21.9.

Encodings:

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A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1954a) Tables of Integral Transforms. Vol. I. McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Notes:

Table errata: Math. Comp. v. 66 (1997), no. 220, p. 1766–1767, v. 65 (1996), no. 215, p. 1384, v. 50 (1988), no. 182, p. 653, v. 41 (1983), no. 164, p. 778–779, v. 27 (1973), no. 122, p. 451, v. 26 (1972), no. 118, p. 599, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 109, p. 239-240.

External Links:

MathReview (H. Kober), ZentralBlatt

Referenced by:

§1.14(viii), §10.22(vi), §10.32(iv), §10.43(vi), §10.9(iv), §11.10(x), §11.5(iii), §11.7(v), §11.9(iv), §12.12, §12.5(iv), §13.10(ii), §13.10(iii), §13.10(iv), §13.23(i), §13.23(ii), §14.17(v), §15.14, §16.20, §16.5, §18.17(ix), §20.10(ii), §20.10(iii), §25.5(ii), §5.13, §6.14(iii), §6.7(iv), §7.14(iii), §7.7(iii), §8.14.

Encodings:

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A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1954b) Tables of Integral Transforms. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Notes:

Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1385, v. 41 (1983), no. 164, pp. 779–780, v. 31 (1977), no. 138, p. 614, v. 31 (1977), no. 137, pp. 328–329, v. 26 (1972), no. 118, p. 599, v. 25 (1971), no. 113, p. 199, v. 23 (1969), no. 106, p. 468.

External Links:

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Referenced by:

§1.14(viii), §10.22(v), §10.22(vi), §10.43(v), §10.43(vi), §12.12, §13.10(v), §13.10(v), §13.10(vi), §13.23(iii), §13.23(v), §15.14, §15.14, §18.17(ix), §5.13, §8.14.

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A. Erdélyi (1941a) Generating functions of certain continuous orthogonal systems. Proc. Roy. Soc. Edinburgh. Sect. A. 61, pp. 61–70.
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External Links:

MathReview (G. Szegő), ZentralBlatt

Referenced by:

§12.16.

Encodings:

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A. Erdélyi (1941b) On Lamé functions. Philos. Mag. (7) 31, pp. 123–130.
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External Links:

MathReview (G. Szegő), ZentralBlatt

Referenced by:

§29.3(ii).

Encodings:

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A. Erdélyi (1941c) On algebraic Lamé functions. Philos. Mag. (7) 32, pp. 348–350.
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External Links:

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Referenced by:

§29.17(ii).

Encodings:

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A. Erdélyi (1942a) Integral equations for Heun functions. Quart. J. Math., Oxford Ser. 13, pp. 107–112.
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External Links:

Document, MathReview (E. Rothe), ZentralBlatt

Referenced by:

§31.10(i).

Encodings:

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A. Erdélyi (1942b) The Fuchsian equation of second order with four singularities. Duke Math. J. 9 (1), pp. 48–58.
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External Links:

Document, MathReview (R. E. Langer), ZentralBlatt

Referenced by:

§31.11(i).

Encodings:

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A. Erdélyi (1944) Certain expansions of solutions of the Heun equation. Quart. J. Math., Oxford Ser. 15, pp. 62–69.
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External Links:

Document, MathReview (R. E. Langer), ZentralBlatt

Referenced by:

§31.11(i), §31.11(i), §31.9(i).

Encodings:

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A. Erdélyi (1956) Asymptotic Expansions. Dover Publications Inc., New York.
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External Links:

MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

Ch.2.

Encodings:

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A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1953a) Higher Transcendental Functions. Vol. I. McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1385, v. 41 (1983), no. 164, p. 778, v. 30 (1976), no. 135, p. 675, v. 25 (1971), no. 115, p. 635, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 112, p. 999, v. 24 (1970), no. 110, p. 504, v. 17 (1963), no. 84, p. 485.

External Links:

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Referenced by:

§13.1, §13.10(ii), §13.10(iv), §13.12, §13.13(i), §13.16(ii), §13.16(iii), §13.23(i), §13.23(ii), §13.25, §13.4(i), §13.4(ii), §13.9(i), §13.9(ii), Ch.13, §14.1, §14.10, §14.12(ii), §14.12(i), §14.12(ii), §14.13, §14.13, §14.17(ii), §14.17(iv), §14.18(ii), §14.18(iii), §14.18(iv), §14.19(i), §14.19(ii), §14.19(iii), §14.19(iv), §14.20(v), §14.21(iii), §14.25, §14.28(i), §14.28(ii), §14.3(iii), §14.3(iii), §14.3(iv), §14.5(iii), §14.5(iv), §14.6(i), §14.6(ii), §14.7(iv), §14.8(i), §14.8(ii), Ch.14, §15.16, §15.4(iii), §15.5(i), §15.6, §15.8(v), §15.8(ii), §15.8(v), §15.9(iii), Ch.15, §16.12, §16.12, §16.13, §16.14(i), §16.14(ii), (16.15.3), §16.15, §16.16(i), §16.16(ii), §16.18, §16.20, §16.20, §16.21, §16.4(ii), §16.5, §16.6, Ch.16, §19.21(i), §19.28, §19.5, §24.16(iii), §24.5(i), §24.7(i), §24.7(ii), §24.8(i), Ch.24, (25.11.12), (25.11.18), §25.11(v), §25.11(vi), (25.12.12), (25.12.13), §25.12(ii), (25.14.1), (25.14.4), (25.14.5), (25.14.6), §25.14(i), §25.14(ii), (25.5.21), (25.5.3), (25.5.8), (25.5.9), §25.5(i), §25.5(iii), (25.8.5), (25.8.6), §25.8, Ch.25, §5.7(i), Ch.5, Notations P, Notations P, Notations Q.

Encodings:

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A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1953b) Higher Transcendental Functions. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 41 (1983), no. 164, p. 778, v. 36 (1981), no. 153, p. 315, v. 30 (1976), no. 135, p. 675, v. 29 (1975), no. 130, p. 670, v. 26 (1972), no. 118, p. 598, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 109, p. 239, v. 17 (1963), no. 84, p. 485.

External Links:

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Referenced by:

§10.22(iv), §10.22(vi), §10.23(iii), §10.23(iii), §10.23(iv), §10.32(i), §10.32(iii), §10.32(iv), §10.43(iv), §10.43(vi), §10.44(iv), §10.60(iv), §10.9(i), §10.9(iii), §10.9(iv), §11.10(vi), §11.4(i), Ch.11, §12.12, §12.12, §12.13(i), §12.5(iv), Ch.12, §18.16(vi), §18.17(i), §18.17(viii), §18.30, §19.1, §19.10(i), §19.14(ii), (19.25.40), §19.25(vi), §19.5, §19.7(ii), §19.9(i), Ch.19, §20.9(i), §22.15(ii), §23.6(iv), Ch.23, §8.13(i), §8.14, §8.3(i), §8.4, §8.6(iii), §8.7, Ch.8, Notations P, Notations P.

Encodings:

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A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1955) Higher Transcendental Functions. Vol. III. McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 41 (1983), no. 164, p. 778.

External Links:

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Referenced by:

§10.46, §27.2(i), Ch.27, Table 28.1.1, §28.10(iii), §28.2(iii), §28.2(v), §29.1, §29.10, §29.11, §29.14, §29.17(i), §29.17(iii), §29.18(i), §29.18(ii), §29.18(iii), §29.18(iii), §29.2(i), §29.2(ii), §29.3(i), §29.3(ii), §29.3(ii), §29.3(iv), §29.5, §29.6(i), §29.6(ii), §29.6(iii), §29.6(iv), §29.8, §29.8, Ch.29, §30.1, §30.10, §30.11(v), §30.11(vi), §30.13(i), §30.14(i), §30.9(iii), Ch.30, §31.2(i), §31.4, §31.5, Ch.31.

Encodings:

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R. Ernvall (1979) Generalized Bernoulli numbers, generalized irregular primes, and class number. Ann. Univ. Turku. Ser. A I 178, pp. 1–72.
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External Links:

ISSN 0082-7002, MathReview (Wells Johnson), ZentralBlatt

Referenced by:

§24.10(ii).

Encodings:

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D. Erricolo and G. Carluccio (2013) Algorithm 934: Fortran 90 subroutines to compute Mathieu functions for complex values of the parameter. ACM Trans. Math. Softw. 40 (1), pp. 8:1–8:19.
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External Links:

ISSN 0098-3500, FullText, Document, MathReview Entry, ZentralBlatt

Referenced by:

4th item, §28.36(iii).

Encodings:

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D. Erricolo (2006) Algorithm 861: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch’s algorithm. ACM Trans. Math. Software 32 (4), pp. 622–634.
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Referenced by:

3rd item, §28.36(iii).

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F. H. L. Essler, H. Frahm, A. R. Its, and V. E. Korepin (1996) Painlevé transcendent describes quantum correlation function of the $X X Z$ antiferromagnet away from the free-fermion point. J. Phys. A 29 (17), pp. 5619–5626.
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External Links:

ISSN 0305-4470, Document, MathReview (Estelle L. Basor), ZentralBlatt

Referenced by:

§32.16.

Encodings:

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T. Estermann (1959) On the representations of a number as a sum of three squares. Proc. London Math. Soc. (3) 9, pp. 575–594.
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External Links:

Document, MathReview (S. Chowla), ZentralBlatt

Referenced by:

§20.12(i).

Encodings:

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Euclid (1908) The Thirteen Books of Euclid’s Elements. Cambridge University Press, Cambridge.
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Notes:

Translated from the text of Heiberg, with introduction and commentary by Thomas L. Heath. Reprint of the Cambridge Univeristy second edition by Dover Publications, Inc., New York, 1956.

External Links:

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Referenced by:

§27.2(i).

Encodings:

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L. Euler (1768) Institutiones Calculi Integralis. Opera Omnia (1), Vol. 11, pp. 110–113.
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Referenced by:

§25.12(i).

Encodings:

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G. A. Evans and J. R. Webster (1999) A comparison of some methods for the evaluation of highly oscillatory integrals. J. Comput. Appl. Math. 112 (1-2), pp. 55–69.
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External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.5(vii).

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W. D. Evans, W. N. Everitt, K. H. Kwon, and L. L. Littlejohn (1993) Real orthogonalizing weights for Bessel polynomials. J. Comput. Appl. Math. 49 (1-3), pp. 51–57.
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External Links:

ISSN 0377-0427, Document, MathReview (B. D. Agrawal), ZentralBlatt

Referenced by:

§18.34(ii).

Encodings:

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W. N. Everitt and D. S. Jones (1977) On an integral inequality. Proc. Roy. Soc. London Ser. A 357, pp. 271–288.
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External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt

Referenced by:

§10.37.

Encodings:

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J. A. Ewell (1990) A new series representation for $\zeta(3)$ . Amer. Math. Monthly 97 (3), pp. 219–220.
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External Links:

ISSN 0002-9890, FullText, MathReview (Christian Radoux), ZentralBlatt

Referenced by:

(25.8.10), §25.8.

Encodings:

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H. Exton (1983) The asymptotic behaviour of the inhomogeneous Airy function ${\rm Hi}(z)$ . Math. Chronicle 12, pp. 99–104.
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External Links:

ISSN 0581-1155, MathReview (Ram Kishore Saxena), ZentralBlatt

Referenced by:

(9.12.24), §9.12(vii).

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