期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 504, 期 2, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2021.125439
关键词
Fractional integration by parts; Hypergeometric function; Integral representation; Saran's function
资金
- Shanghai Sailing Program [19YF1400100]
- Science and Technology Commission of Shanghai Municipality [18dz2271000]
Motivated by recent applications in physics and statistics, this study further investigates Saran's work on the hypergeometric function FK. The analytic continuation and asymptotics of FK are obtained through a new single contour integral representation, and a new integral identity is proved using fractional integration by parts. Various special cases and their relationship with Koschmieder's work are discussed in detail.
Motivated by some recent applications of a certain triple series hypergeometric function in the areas of physics and statistics, we investigate further Saran's work (e.g., [Acta Math. 93 (1955), 293-312]) related to this useful hypergeometric function FK. Its analytic continuation and asymptotics are obtained by establishing a new single contour integral representation. With the help of the fractional integration by parts, we prove a new integral identity and discuss in detail its various special cases and their relationship with Koschmieder's work [Acta Math. 79 (1947), 241-254]. Several consequences and special cases of the results presented in this paper are also mentioned. (C) 2021 Elsevier Inc. All rights reserved.
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