Index A

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

Abel-Plana formula§2.10(i)
additive number theoryCh.27, §27.14(vi)
- Dedekind modular function§27.14(iv)
- Dedekind sum§27.14(iii)
- discriminant function§27.14(vi)
- Euler's pentagonal number theorem§27.14(ii)
- Goldbach conjecture§27.13(ii)
- Jacobi's identities§27.13(iv)
- notation§27.1
- partition function§27.13(i)
  - unrestricted§27.14(i)
- Ramanujan's identity§27.14(v)
- Ramanujan's tau function§27.14(vi)
- representation by squares§27.13(iv)
- Waring's problem§27.13(iii)
Airy functions§9.1
- analytic properties§9.2(i)
- applications
  - mathematical§9.15
  - physical§9.16, §9.16
- approximations
  - expansions in Chebyshev series§9.19(ii)
  - in terms of elementary functions§9.19(i)
  - in the complex plane§9.19(iii)
- asymptotic expansions§9.7, §9.7(v)
  - error bounds§9.7(iii), §9.7(iv)
  - exponentially-improved§9.7(v)
- computation§9.17, §9.17(v)
- connection formulas§9.2(v)
- definitions§9.2(i)
- differential equation§9.2(i)
  - for products§9.11(i)
  - initial values§9.2(ii)
  - numerically satisfactory solutions§9.2(iii)
  - Riccati form§9.2(vi)
- envelope functions§2.8(iii)
- generalizedsee generalized Airy functions
- graphics§9.3, §9.3(ii)
- incomplete§9.14
- integral representations§9.11(iii), §9.5(i), §9.5(ii)
- integrals
  - approximations§9.19(i), §9.19(ii), §9.19(ii), §9.19(i), §9.19(ii), §9.19(iii)
  - asymptotic approximations§9.10(ii)
  - definite§9.10(iv)
  - indefinite§9.10(i)
  - of products§9.11(iv), §9.11(v)
  - repeated§9.10(viii)
  - tables§9.18(v)
- Laplace transforms§9.10(v)
- Maclaurin series§9.4
- Mellin transform§9.10(vi)
- modulus and phase
  - asymptotic expansions§9.8(iv), §9.8(iv)
  - definitions§9.8(i)
  - graphs§9.3(i)
  - identities§9.8(ii)
  - monotonicity§9.8(iii)
  - relation to Bessel functions§9.8(i)
  - relation to zeros§9.9(ii)
- notation§9.1
- products
  - differential equation§9.11(i)
  - integral representations§9.11(iii)
  - integrals§9.11(iv), §9.11(v)
  - Wronskian§9.11(ii)
- relation to Bessel functions and modified Bessel functions§9.6, §9.6(ii)
- relation to confluent hypergeometric functions§9.6(iii)
- Stieltjes transforms§9.10(vii)
- tables
  - complex variables§9.18(iii)
  - integrals§9.18(v)
  - real variables§9.18(ii)
  - zeros§9.18(iv), §9.9(v)
- Wronskians§9.2(iv)
- zeros
  - asymptotic expansions§9.9(iv)
  - computation§9.17(v)
  - differentiation§9.9(iii)
  - relation to modulus and phase§9.9(ii)
  - tables§9.18(iv), §9.9(v)
Airy's equationsee
Airy transform§9.10(ix)
angular momenta§34.2
angular momentum coupling coefficientssee
arithmetic Fourier transform§27.17

asymptotic and order symbols§2.1(i)
- definition§2.1(i)
- differentiation§2.1(ii)
- integration§2.1(ii)
asymptotic approximations and expansionssee
- algebraic operations§2.1(iii)
- cases of failure§2.11(i), §2.11(i), §2.6(i)
- differentiation§2.1(iii)
- exponentially-improved expansions§2.11(iii), §2.11(v)
- generalized§2.1(v)
- hyperasymptotic expansions§2.11(v)
- improved accuracy via numerical transformations§2.11(vi)
- integration§2.1(iii)
- logarithms of§2.1(iii)
- null§2.1(iii)
- numerical use of§2.11(i), §2.11(vi)
- Poincaré type§2.1(iii)
- powers of§2.1(iii)
- re-expansion of remainder terms§2.11(iii), §2.11(vi)
- reversion of§2.2
- Stokes phenomenon§2.11(iv)
- substitution of§2.1(iii)
- uniform§2.1(iv)
- uniqueness§2.1(iii)
- via connection formulas§2.11(ii)
asymptotic approximations of integrals§2.2, §2.6(iv)
- Bleistein's method§2.3(v)
- Chester-Friedman-Ursell method§2.4(v)
- coalescing critical points§2.4(v), §2.4(vi)
- coalescing peak and endpoint§2.3(v)
- coalescing saddle points§2.4(v)
- distributional methods§2.6, §2.6(iv)
- Fourier integrals§2.3(i)
- Haar's method§2.4(ii)
- integration by parts§2.3(i)
- inverse Laplace transforms§2.4(i), §2.4(ii)
- Laplace's method§2.3(iii), §2.4(iii)
- Laplace transforms§2.3(i)
- Mellin transform methods§2.5
  - extensions§2.5(ii)
- method of stationary phase§2.3(iv)
  - extensions§2.3(iv)
- method of steepest descents§2.4(iv)
- multidimensional integrals§2.5(ii)
- Stieltjes transforms§2.6(ii)
  - generalized§2.6(ii)
- Watson's lemma§2.3(ii), §2.4(i)
  - generalized§2.3(ii)
asymptotic approximations of sums and sequences§2.10, §2.10(iv)
- Abel-Plana formula§2.10(i)
- Darboux's method§2.10(iv), §2.10(iv)
- entire functions§2.10(iii)
- Euler-Maclaurin formula§2.10(i), §2.10(i)
- summation by parts§2.10(ii)
asymptotic scale or sequence§2.1(v)
asymptotic solutions of difference equations§2.9, §2.9(iii)
- characteristic equation§2.9(i)
- coincident characteristic values§2.9(ii)
- Liouville-Green (or WKBJ) type approximations§2.9(iii)
- transition points§2.9(iii)
- turning points§2.9(iii)
- with a parameter§2.9(ii)
asymptotic solutions of differential equations§2.6(iv), §2.8(vi)
- characteristic equation§2.7(ii)
- coincident characteristic values§2.7(ii)
- error-control function§2.7(iii)
- Fabry's transformation§2.7(ii)
- irregular singularities of rank 1§2.7(ii)
- Liouville-Green approximation theorem§2.7(iii)
- Liouville-Green (or WKBJ) approximations§2.7(iii), §2.7(iii)
- numerically satisfactory solutions§2.7(iv)
- resurgence§2.11(v), §2.7(ii)
- with a parameter§2.8, §2.8(vi)
  - classification of cases§2.8(i)
  - coalescing transition points§2.8(vi)
  - connection formulas across transition points§2.8(v)
  - in terms of Airy functions§2.8(iii)
  - in terms of Bessel functions of fixed order§2.8(iv)
  - in terms of Bessel functions of variable order§2.8(vi)
  - in terms of elementary functions§2.8(ii)
  - Liouville transformation§2.8(i)
  - transition points§2.8(i)
  - turning points§2.8(i)
asymptotic solutions of transcendental equations§2.2
- Lagrange's formula§2.2
atomic spectroscopy
- $3j,6j,9j$ symbols§34.12