Certain Integral Formulae Associated with the Product of Generalized Hypergeometric Series and Several Elementary Functions Derived from Formulas for the Beta Function

Symmetry

卷:14

Adem Kilicman¹  Shantha Kumari Kurumujji²  Junesang Choi³  Arjun Kumar Rathie⁴ 

[1] Department of Mathematics and Statistics, Institute for Mathematical Research, University Putra Malaysia, UPM, Serdang 43400, Selangor, Malaysia;

[2] Department of Mathematics, AJ Institute of Engineering and Technology (Visvesvaraya Technological University (VTU)), Mangaluru 575006, India;

[3] Department of Mathematics, Dongguk University, Gyeongju 38066, Korea;

[4] Department of Mathematics, Vedant College of Engineering & Technology (Rajasthan Technical University), Kota 324010, India;

关键词: gamma function;    beta function;    generalized hypergeometric functions _pF_q;    summation formulas for _pF_q;   

DOI  :  10.3390/sym14020389

来源: DOAJ

【 摘 要 】

The literature has an astonishingly large number of integral formulae involving a range of special functions. In this paper, by using three Beta function formulae, we aim to establish three integral formulas whose integrands are products of the generalized hypergeometric series ${}_{p+1}{F}_p$ and the integrands of the three Beta function formulae. Among the many particular instances for our formulae, several are stated clearly. Moreover, an intriguing inequality that emerges throughout the proving procedure is shown. It is worth noting that the three integral formulae shown here may be expanded further by using a variety of more generalized special functions than ${}_{p+1}{F}_p$. Symmetry occurs naturally in the Beta and ${}_{p+1}{F}_p$ functions, which are two of the most important functions discussed in this study.

【 授权许可】

Unknown