Index U
-
ultraspherical polynomials §18.3, see also classical orthogonal polynomials.
- addition theorem ¶ ‣ §18.18(ii)
-
applications
- zonal spherical harmonics ¶ ‣ §18.38(ii)
- asymptotic approximations §18.15(ii)
-
case
§18.1(iii)
- computation Ch.18
- definition Table 18.3.1
- derivatives ¶ ‣ §18.9(iii)
- differential equation Table 18.8.1
- expansions in series of ¶ ‣ §18.18(iv), ¶ ‣ §18.18(v), ¶ ‣ §18.18(viii)
- Fourier transforms ¶ ‣ §18.17(v)
- generating functions ¶ ‣ §18.12
- inequalities ¶ ‣ §18.14(i)
-
integral representations ¶ ‣ §18.10(i), ¶ ‣ §18.10(ii), Table 18.10.1
- for products ¶ ‣ §18.17(ii)
- integrals ¶ ‣ §18.17(iv)
- interrelations with other orthogonal polynomials ¶ ‣ §18.11(i), §18.7, ¶ ‣ §18.7(iii)
- leading coefficients Table 18.3.1
- limits to monomials §18.6(ii)
- linearization formula ¶ ‣ §18.18(v)
- Mellin transform ¶ ‣ §18.17(vii)
- normalization Table 18.3.1
- notation ¶ ‣ §18.1(ii), §18.1(iii)
- orthogonality property Table 18.3.1
- parameter constraint Table 18.3.1, ¶ ‣ §18.5(iii)
- recurrence relations Table 18.9.1
-
relations to other functions
- Ferrers functions ¶ ‣ §18.11(i)
- hypergeometric function ¶ ‣ §15.9(i), §18.5(iii)
- Rodrigues formula Table 18.5.1
- special values Table 18.6.1
- symmetry Table 18.6.1
- tables of coefficients §18.3
- upper bound ¶ ‣ §18.14(i)
- weight function Table 18.3.1
- zeros §18.16(iii), §18.2(vi)
-
umbilics
- normal forms ¶ ‣ §36.2(i)
-
umbral calculus
- Bernoulli and Euler polynomials §24.4(viii)
-
uniformization
- algebraic equations via Jacobian elliptic functions §22.18(iii)
-
unity
- roots of §1.11(iv)