Kummer transformation

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21: 10.22 Integrals

… ►For the confluent hypergeometric function $𝐌$ see §13.2(i). … ►

§10.22(v) Hankel Transform

►The Hankel transform (or Bessel transform) of a function $f(x)$ is defined as … ►The following two formulas are generalizations of the Hankel transform. …This is the Weber transform. …

22: 17.6 ${}_2{}^{}\varphi _1^{}$ Function

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Bailey–Daum $q$-Kummer Sum

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Heine’s First Transformation

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Heine’s Third Transformation

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Fine’s Second Transformation

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Fine’s Third Transformation

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23: Bibliography L

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Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions. Comput. Phys. Comm. 99 (2-3), pp. 297–306.

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Notes:

Single-precision Fortran, maximum accuracy 8S.

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ISSN 0010-4655, Document, Code, ZentralBlatt

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4th item.

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Asymptotics of the first Appell function $F_1$ with large parameters II. Integral Transforms Spec. Funct. 24 (12), pp. 982–999.

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ISSN 1065-2469, Document, FullText, MathReview Entry, ZentralBlatt

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§16.13, §16.13.

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Asymptotics of the first Appell function $F_1$ with large parameters. Integral Transforms Spec. Funct. 24 (9), pp. 715–733.

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External Links:

ISSN 1065-2469, Document, FullText, MathReview Entry, ZentralBlatt

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§16.13, §16.13.

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Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions. Numer. Math. 116 (2), pp. 269–289.

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ISSN 0029-599X, Document, FullText, MathReview (Richard B. Paris), ZentralBlatt

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§13.11, §13.11.

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Bessel transforms and rational extrapolation. Numer. Math. 47 (1), pp. 1–14.

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ISSN 0029-599X, Document, MathReview (Vítĕzslav Veselý), ZentralBlatt

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§10.74(vii).

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24: Bibliography

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Solitons and the Inverse Scattering Transform. SIAM Studies in Applied Mathematics, Vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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ISBN 0-89871-174-6, MathReview (Benno Fuchssteiner), ZentralBlatt

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§21.9, §21.9, §32.5, §9.16, Profile Mark J. Ablowitz.

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Lectures on Integral Transforms. Translations of Mathematical Monographs, Vol. 70, American Mathematical Society, Providence, RI.

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Notes:

Translated from the Russian by H. H. McFaden

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ISBN 0-8218-4524-1, MathReview, ZentralBlatt

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§10.22(v).

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Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule. Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.

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ISSN 0373-1243, MathReview, ZentralBlatt

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§13.29(iii).

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Algorithm 588. Fast Hankel transforms using related and lagged convolutions. ACM Trans. Math. Software 8 (4), pp. 369–370.

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Notes:

Single-precision Fortran, maximum accuracy 8S.

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ISSN 0098-3500, Document, GAMS (module 588; package TOMS)

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2nd item.

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Summations and transformations for basic Appell series. J. London Math. Soc. (2) 4, pp. 618–622.

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External Links:

MathReview (R. N. Jain), ZentralBlatt

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§17.11.

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