relation to infinite double series

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11: 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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Asymptotic and numeric study of eigenvalues of the double confluent Heun equation. J. Phys. A 31 (42), pp. 8521–8531.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

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§31.13, §31.18.

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On the theory of diffraction by an aperture in an infinite plane screen. I. Phys. Rev. 74 (8), pp. 958–974.

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Document, MathReview (C. J. Bouwkamp), ZentralBlatt

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§11.12.

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Monotonic sequences related to zeros of Bessel functions. Numer. Algorithms 49 (1-4), pp. 221–233.

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ISSN 1017-1398, Document, FullText, MathReview (Javier Segura), ZentralBlatt

Referenced by:

§10.21(iv), §10.21(iv).

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Integrating some infinite oscillating tails. J. Comput. Appl. Math. 12/13, pp. 109–117.

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ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.5(vii).

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12: Bibliography O

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Summing one- and two-dimensional series related to the Euler series. J. Comput. Appl. Math. 98 (2), pp. 245–271.

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ISSN 0377-0427, Document, MathReview (Boris Petrovich Osilenker), ZentralBlatt

Referenced by:

§25.8.

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Complete elliptic integrals resulting from infinite integrals of Bessel functions. J. Res. Nat. Bur. Standards Sect. B 78B (3), pp. 113–135.

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ISSN 0160-1741, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

§10.22(vi), §10.43(vi).

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Complete elliptic integrals resulting from infinite integrals of Bessel functions. II. J. Res. Nat. Bur. Standards Sect. B 79B (3-4), pp. 137–170.

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ISSN 0160-1741, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

§10.22(vi), §10.43(vi).

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Associated Legendre functions on the cut. J. Comput. Phys. 51 (3), pp. 502–518.

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Notes:

Includes single, double precision Fortran code.

External Links:

GAMS (module DXNRMP; package SLATEC), ISSN 0021-9991, Document, MathReview (G. P. Bhattacharjee), ZentralBlatt

Referenced by:

§14.32, 7th item.

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A closed form solution of the $s$-wave Bethe-Goldstone equation with an infinite repulsive core. J. Math. Phys. 27 (4), pp. 1154–1158.

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ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§30.13(v).

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13: Errata

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Section: 15.9(v) Complete Elliptic Integrals. Equations: (11.11.9_5), (11.11.13_5), Intermediate equality in (15.4.27) which relates to $F(a,a;a+1;\frac{1}{2})$, (15.4.34), (19.5.4_1), (19.5.4_2) and (19.5.4_3).

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In ¶IEEE Standard (in §3.1(i)), the description was modified to reflect the most recent IEEE 754-2019 Floating-Point Arithmetic Standard IEEE (2019). In the new standard, single, double and quad floating-point precisions are replaced with new standard names of binary32, binary64 and binary128. Figure 3.1.1 has been expanded to include the binary128 floating-point memory positions and the caption has been updated using the terminology of the 2019 standard. A sentence at the end of Subsection 3.1(ii) has been added referring readers to the IEEE Standards for Interval Arithmetic IEEE (2015, 2018).

Suggested by Nicola Torracca.

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It is now mentioned that (25.2.5), defines the Stieltjes constants ${\gamma }_n$. Consequently, ${\gamma }_n$ in (25.2.4), (25.6.12) are now identified as the Stieltjes constants.

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The Kronecker delta symbols have been moved furthest to the right, as is common convention for orthogonality relations.

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A number of additions and changes have been made to the metadata to reflect new and changed references as well as to how some equations have been derived.

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14: Bibliography M

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Algorithm 757: MISCFUN, a software package to compute uncommon special functions. ACM Trans. Math. Software 22 (3), pp. 288–301.

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Notes:

Double-precision Fortran, maximum accuracy 20D.

External Links:

ISSN 0098-3500, Document, GAMS (module 757; package TOMS), MathReview Entry, ZentralBlatt

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5th item, 1st item, 1st item, 4th item, 1st item, 1st item.

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Connection between quantum systems involving the fourth Painlevé transcendent and $k$-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial. J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..

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ISSN 0022-2488, Document, Link, MathReview Entry

Referenced by:

§18.38(iii).

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A new symmetry related to $\mathrm{𝑆𝑈}(n)$ for classical basic hypergeometric series. Adv. in Math. 57 (1), pp. 71–90.

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ISSN 0001-8708, Document, MathReview (George E. Andrews), ZentralBlatt

Referenced by:

§17.15.

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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Ramanujan J. 6 (1), pp. 7–149.

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Document, ZentralBlatt

Referenced by:

§27.13(iv).

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Further improvements of some double inequalities for bounding the gamma function. Math. Comput. Modelling 57 (5-6), pp. 1360–1363.

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ISSN 0895-7177, Document, FullText, MathReview (Emil C. Popa)

Referenced by:

§5.6(i).

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