Appell functions

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11—18 of 18 matching pages

11: 19.25 Relations to Other Functions

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§19.25(vii) Hypergeometric Function

… ►For these results and extensions to the Appell function

{F_{1}}

(§16.13) and Lauricella’s function

F_{D}

see Carlson (1963). (

{F_{1}}

and

F_{D}

are equivalent to the

R

-function of 3 and

n

variables, respectively, but lack full symmetry.)

12: Bibliography F

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C. Ferreira, J. L. López, and E. Pérez Sinusía (2013a) The third Appell function for one large variable. J. Approx. Theory 165, pp. 60–69.

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External Links:: ISSN 0021-9045, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §16.13, §16.13.
Encodings:: BibTeX

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C. Ferreira, J. L. López, and E. P. Sinusía (2013b) The second Appell function for one large variable. Mediterr. J. Math. 10 (4), pp. 1853–1865.

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External Links:: ISSN 1660-5446, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §16.13, §16.13.
Encodings:: BibTeX

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13: Bibliography L

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J. L. López, P. Pagola, and E. Pérez Sinusía (2013a) 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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External Links:: ISSN 1065-2469, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §16.13, §16.13.
Encodings:: BibTeX

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J. L. López, P. Pagola, and E. Pérez Sinusía (2013b) 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
Referenced by:: §16.13, §16.13.
Encodings:: BibTeX

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14: Bibliography C

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B. C. Carlson (1976) Quadratic transformations of Appell functions. SIAM J. Math. Anal. 7 (2), pp. 291–304.

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External Links:: Document, MathReview (L. J. Slater), ZentralBlatt
Referenced by:: §16.16(ii), §19.22(i).
Encodings:: BibTeX

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15: Bibliography B

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J. L. Burchnall and T. W. Chaundy (1940) Expansions of Appell’s double hypergeometric functions. Quart. J. Math., Oxford Ser. 11, pp. 249–270.

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External Links:: Document, MathReview (G. Szegő), ZentralBlatt
Referenced by:: §15.16, (16.15.4), §16.15, §16.16(i).
Encodings:: BibTeX

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J. L. Burchnall and T. W. Chaundy (1941) Expansions of Appell’s double hypergeometric functions. II. Quart. J. Math., Oxford Ser. 12, pp. 112–128.

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External Links:: Document, MathReview (G. Szegő), ZentralBlatt
Referenced by:: §16.16(i).
Encodings:: BibTeX

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The notation used for the $q$ -Appell functions in Equations (17.4.5), (17.4.6),(17.4.7), (17.4.8), (17.11.1), (17.11.2) and (17.11.3) was updated to explicitly include the argument $q$ , as used in Gasper and Rahman (2004).

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17: 16 Generalized Hypergeometric Functions & Meijer G-Function

Chapter 16 Generalized Hypergeometric Functions and Meijer $G$ -Function

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18: Bibliography

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M. Abramowitz (1954) Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions. J. Math. Physics 33, pp. 111–116.

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External Links:: MathReview (E. Weber), ZentralBlatt
Referenced by:: §33.9(ii).
Encodings:: BibTeX

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Z. Altaç (1996) Integrals involving Bickley and Bessel functions in radiative transfer, and generalized exponential integral functions. J. Heat Transfer 118 (3), pp. 789–792.

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External Links:: Document
Referenced by:: §10.73(iv), §8.24(iii).
Encodings:: BibTeX

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G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen (1992a) Functional inequalities for hypergeometric functions and complete elliptic integrals. SIAM J. Math. Anal. 23 (2), pp. 512–524.

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External Links:: ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt
Referenced by:: §19.9(i).
Encodings:: BibTeX

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G. E. Andrews (1972) 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
Referenced by:: §17.11.
Encodings:: BibTeX

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P. Appell and J. Kampé de Fériet (1926) Fonctions hypergéométriques et hypersphériques. Polynomes d’Hermite. Gauthier-Villars, Paris.

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External Links:: ZentralBlatt
Referenced by:: §16.13, §16.15, Ch.16.
Encodings:: BibTeX

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