expansions in series of spherical Bessel functions

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21: Bibliography K

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Series expansions for the third incomplete elliptic integral via partial fraction decompositions. J. Comput. Appl. Math. 207 (2), pp. 331–337.

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ISSN 0377-0427, Document, MathReview (José Luis López), ZentralBlatt

Referenced by:

§19.12, §19.5.

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Asymptotic expansions of certain $q$-series and a formula of Ramanujan for specific values of the Riemann zeta function. Acta Arith. 107 (3), pp. 269–298.

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ISSN 0065-1036, Document, Link, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§17.2(i).

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Calculation of modified Bessel functions in a complex domain. Zh. Vychisl. Mat. i Mat. Fiz. 24 (5), pp. 650–664.

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Notes:

English translation in U.S.S.R. Computational Math. and Math. Phys. 24(3), pp. 15–24

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ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.42, §10.74(iv).

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On multiple zeros of derivatives of Bessel’s cylindrical functions. Dokl. Akad. Nauk SSSR 288 (2), pp. 285–288 (Russian).

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Notes:

In Russian. English translation: Soviet Math. Dokl. 33(3), 650–653, (1986).

External Links:

ISSN 0002-3264, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.21(i), §10.74(vi).

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Askey-Wilson polynomials as zonal spherical functions on the $\mathrm{SU}(2)$ quantum group. SIAM J. Math. Anal. 24 (3), pp. 795–813.

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ISSN 0036-1410, Document, Link, MathReview Entry

Referenced by:

(18.28.27).

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22: Bibliography L

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New method to obtain small parameter power series expansions of Mathieu radial and angular functions. Math. Comp. 78 (265), pp. 255–274.

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ISSN 0025-5718, Document, FullText, MathReview (Junesang Choi), ZentralBlatt

Referenced by:

§28.24, §28.24.

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Numerical evaluation of integrals containing a spherical Bessel function by product integration. J. Math. Phys. 22 (7), pp. 1399–1413.

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ISSN 0022-2488, Document, MathReview (C. W. Clenshaw), ZentralBlatt

Referenced by:

§10.74(vii).

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New series expansions for the confluent hypergeometric function $M(a,b,z)$ . Appl. Math. Comput. 235, pp. 26–31.

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ISSN 0096-3003, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§13.11, §13.11.

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New series expansions of the Gauss hypergeometric function. Adv. Comput. Math. 39 (2), pp. 349–365.

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ISSN 1019-7168, Document, FullText, MathReview (Jochen Denzler), ZentralBlatt

Referenced by:

§15.19(i), §15.19(i).

Encodings:

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Expansion of the confluent hypergeometric function in series of Bessel functions. Math. Tables Aids Comput. 13 (68), pp. 261–271.

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External Links:

FullText, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§13.24(ii).

Encodings:

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23: 18.17 Integrals

… ►and three formulas similar to (18.17.9)–(18.17.11) by symmetry; compare the second row in Table 18.6.1. … ►In particular, in case of exponential Fourier transforms, we may assume $y\in ℝ$. … ►For the Bessel function $J_{\nu }$ see §10.2(ii). … ►In (18.17.21_1) the branch choice of $\sqrt{2c-1}$ for is unimportant because on the right-hand side only even powers of $\sqrt{2c-1}$ occur after expansion of the Hermite polynomial by (18.5.13). … ►Many of the Fourier transforms given in §18.17(v) have analytic continuations to Laplace transforms. …

24: 18.3 Definitions

§18.3 Definitions

… ►For finite power series of the Jacobi, ultraspherical, Laguerre, and Hermite polynomials, see §18.5(iii) (in powers of $x-1$ for Jacobi polynomials, in powers of $x$ for the other cases). Explicit power series for Chebyshev, Legendre, Laguerre, and Hermite polynomials for $n=0,1,\mathrm{\dots },6$ are given in §18.5(iv). … ►

Bessel polynomials

►Bessel polynomials are often included among the classical OP’s. …