JOURNAL BROWSE
Search
Advanced SearchSearch Tips
CERTAIN DECOMPOSITION FORMULAS OF GENERALIZED HYPERGEOMETRIC FUNCTIONS pFq AND SOME FORMULAS OF AN ANALYTIC CONTINUATION OF THE CLAUSEN FUNCTION 3F2
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
CERTAIN DECOMPOSITION FORMULAS OF GENERALIZED HYPERGEOMETRIC FUNCTIONS pFq AND SOME FORMULAS OF AN ANALYTIC CONTINUATION OF THE CLAUSEN FUNCTION 3F2
Choi, June-Sang; Hasanov, Anvar;
  PDF(new window)
 Abstract
Here, by using the symbolical method introduced by Burchnall and Chaundy, we aim at constructing certain expansion formulas for the generalized hypergeometric function . In addition, using our expansion formulas for , we present formulas of an analytic continuation of the Clausen hypergeometric function , which are much simpler than an earlier known result. We also give some integral representations for .
 Keywords
generalized hypergeometric series;inverse pairs of symbolic;decomposition formulas;Gauss function;Clausen function;formulas of analytic continuations;
 Language
English
 Cited by
1.
DECOMPOSITION FORMULAE FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS WITH THE GAUSS-KUMMER IDENTITY,;;

대한수학회논문집, 2014. vol.29. 1, pp.97-108 crossref(new window)
1.
DECOMPOSITION FORMULAE FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS WITH THE GAUSS-KUMMER IDENTITY, Communications of the Korean Mathematical Society, 2014, 29, 1, 97  crossref(new windwow)
 References
1.
P. Appell and J. Kampe de Feriet, Fonctions Hypergeometriques et Hyperspheriques; Polynomes d'Hermite, Gauthier - Villars, Paris, 1926.

2.
J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric functions, Quart. J. Math. Oxford Ser. 11 (1940), 249-270. crossref(new window)

3.
J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric functions. II, Quart. J. Math. Oxford Ser. 12 (1941), 112-128. crossref(new window)

4.
T. W. Chaundy, Expansions of hypergeometric functions, Quart. J. Math. Oxford Ser. 13 (1942), 159-171. crossref(new window)

5.
A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions Vols. I, II, Based, in part, on notes left by Harry Bateman. McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953.

6.
A. Hasanov and H. M. Srivastava, Some decomposition formulas associated with the Lauricella function $F^{(\tau)}_A$ A and other multiple hypergeometric functions, Appl. Math. Lett. 19 (2006), no. 2, 113-121. crossref(new window)

7.
A. Hasanov and H. M. Srivastava, Decomposition formulas associated with the lauricella multivariable hypergeo-metric functions, Comput. Math. Appl. 53 (2007), no. 7, 1119-1128. crossref(new window)

8.
O. I. Marichev, Handbook of Integral Transforms of Higher Transcendental Functions, Halsted Press (Ellis Horwood Limited, Chichester), Wiley, New York, Chichester, Brisbane and Toronto, 1982.

9.
P. O. M. Olsson, Analytic continuations of higher-order hypergeometric functions, J. Math. Phys. 7 (1966), no. 4, 702-710. crossref(new window)

10.
R. C. Pandey, On the expansions of hypergeometric functions, Agra Univ. J. Res. Sci. 12 (1963), 159-169.

11.
E. G. Poole, Introduction to the Theory of Linear Differential Equations, Clarendon (Oxford University Press), Oxford, 1936.

12.
E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.

13.
J. P. Singhal and S. S. Bhati, Certain expansions associated with hypergeometric functions n variables, Glasnik Mat. Ser. III 11 (31) (1976), no. 2, 239-245.

14.
H. M. Srivastava, Some integrals representing triple hypergeometric functions, Rend. Circ. Mat. Palermo (Ser. 2) 16 (1967), 99-115. crossref(new window)

15.
H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), Wiley, New York, Chichester, Brisbane and Toronto, 1985.

16.
H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), Wiley, New York, Chichester, Brisbane and Toronto, 1984.