NEW RESULTS FOR THE SERIES 2F1(x) WITH AN APPLICATION
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The well known quadratic transformation formula due to Gauss: [수식] plays an important role in the theory of (generalized) hypergeometric series. In 2001, Rathie and Kim have obtained two results closely related to the above quadratic transformation for 2F1. Our main objective of this paper is to deduce some interesting known or new results for the series 2F1(x) by using the above Gauss’s quadratic transformation and its contiguous relations and then apply our results to provide a list of a large number of integrals involving confluent hypergeometric functions, some of which are (presumably) new. The results established here are (potentially) useful in mathematics, physics, statistics, engineering, and so on.
Abstract
The well known quadratic transformation formula due to Gauss: [수식] plays an important role in the theory of (generalized) hypergeometric series. In 2001, Rathie and Kim have obtained two results closely related to the above quadratic transformation for 2F1. Our main objective of this paper is to deduce some interesting known or new results for the series 2F1(x) by using the above Gauss’s quadratic transformation and its contiguous relations and then apply our results to provide a list of a large number of integrals involving confluent hypergeometric functions, some of which are (presumably) new. The results established here are (potentially) useful in mathematics, physics, statistics, engineering, and so on.
참고문헌 (21)
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