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- Title
r-Confluent Hypergeometric Functions and Their Applications.
- Authors
Virchenko, N. O.; Didychenko, Ie. V.
- Abstract
The new properties of the r-generalized confluent hypergeometric functions are investigated. The integral representations, the representation by series are constructed. Applications of these functions to the calculation of integrals absent in cash scientific and reference mathematical literature are given. Applications of the r-confluent hypergeometric functions in the theory of the special functions are considered, in partial, the r-generalized gamma-functions, incomplete gamma-functions, the r-generalized beta-functions, the r-generalized ζ-functions, Volterra functions and contiguous to them are introduced, their basic properties are investigated. The theorems of addition, multiplication for r-generalized hypergeometric function are proved. The interesting generalization of Ramanujan formula involving r-generalized confluent hypergeometric function and r-generalized beta-function. This formula gives the possibility to calculate the new complicated improper integrals.
- Subjects
COULOMB functions; MATHEMATICS theorems; INTEGRAL representations; MATHEMATICAL literature; BETA functions; MULTIPLICATION; ADDITIVE functions
- Publication
Naukovi visti NTUU - KPI, 2012, Vol 84, Issue 4, p20
- ISSN
1810-0546
- Publication type
Article