Confluent expansions for functions of two variables
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- by V. L. Deshpande PDF
- Math. Comp. 28 (1974), 605-611 Request permission
Abstract:
In a recent paper, J. L. Fields established four theorems giving confluent expansions for functions of one variable. In the present paper, we extended one theorem of Fields for functions of two variables. The usefulness of the theorem is illustrated by obtaining known and hitherto unknown transformations for Appell functions and Horn functions.References
- V. L. Deshpande, Theorems involving confluent asymptotic expansions of functions of two variables, An. Univ. Timişoara Ser. Şti. Mat. 8 (1970), 143–151 (English, with Romanian summary). MR 326029 V. L. Deshpande, "Theorems on asymptotic confluent expansions for functions of two variables," J. Natur. Sci. and Math., v. 11, 1971, no. 1.
- V. M. Bhise and V. L. Deshpande, On asymptotic confluent expansions for functions of two variables, Nederl. Akad. Wetensch. Proc. Ser. A 75=Indag. Math. 34 (1972), 106–112. MR 0330526
- Jerry L. Fields, Confluent expansions, Math. Comp. 21 (1967), 189–197. MR 224880, DOI 10.1090/S0025-5718-1967-0224880-7 A. Erdélyi, Higher Transcendental Functions. Vol. I. The Hypergeometric Function, Legendre Functions, McGraw-Hill, New York, 1953. MR 15, 419. P. Appell & J. Kampé de Fériet, Fonctions hypergéométriques et hypersphériques polynômes d’Hermite, Gauthier-Villars, Paris, 1926.
- F. G. Tricomi and A. Erdélyi, The asymptotic expansion of a ratio of gamma functions, Pacific J. Math. 1 (1951), 133–142. MR 43948
- Earl D. Rainville, Special functions, The Macmillan Company, New York, 1960. MR 0107725
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 605-611
- MSC: Primary 33A30
- DOI: https://doi.org/10.1090/S0025-5718-1974-0340657-X
- MathSciNet review: 0340657