Extended Srivastava’s triple hypergeometric HA,p,q function and related bounding inequalities

被引：0
作者：
R. K. Parmar
T. K. Pogány
机构：
[1] Government College of Engineering and Technology,
[2] University of Rijeka,undefined
[3] Óbuda University,undefined
来源：
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) | 2017年 / 52卷
关键词：
(p, q)-extended Beta function; (p, q)-extended hypergeometric function; extended Appell function; Mellin transform; Laguerre polynomial; bounding inequality; 33B20; 33C20; 33B15; 33C05;
D O I：
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学科分类号：
摘要：
In this paper, motivated by certain recent extensions of the Euler’s beta, Gauss’ hypergeometric and confluent hypergeometric functions (see [4]), we extend the Srivastava’s triple hypergeometric function HA by making use of two additional parameters in the integrand. Systematic investigation of its properties including, among others, various integral representations of Euler and Laplace type, Mellin transforms, Laguerre polynomial representation, transformation formulas and a recurrence relation, is presented. Also, by virtue of Luke’s bounds for hypergeometric functions and various bounds upon the Bessel functions appearing in the kernels of the newly established integral representations, we deduce a set of bounding inequalities for the extended Srivastava’s triple hypergeometric function HA,p,q.
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页码：276 / 287
页数：11
相关论文
共 29 条
  • [1] Chaudhry M. A.(1997)Extension of Euler’s Beta function J. Comput. Appl. Math. 78 19-32
  • [2] Qadir A.(2004)Extended hypergeometric and confluent hypergeometric functions Appl. Math. Comput. 159 589-602
  • [3] Rafique M.(2014)Extension of extended beta, hypergeometric and confluent hypergeometric functions Honam Math. J. 36 357-385
  • [4] Zubair S. M.(2006)Uniform bounds for Bessel functions J. Appl. Anal. 12 83-91
  • [5] Chaudhry M. A.(2014)Approximations for the Bessel and Airy functions with an explicit error term LMS J. Comput. Math. 17 209-225
  • [6] Qadir A.(2014)On the Bessel function LMSJ. Comput. Math. 17 273-281
  • [7] Srivastava H. M.(1884)( Abh. der math. phys. Classe der k. b. Akad. derWiss. (München) 15 229-328
  • [8] Paris R. B.(1884)) in the transition region Abh. der math. phys. Classe der k. b. Akad. derWiss. (München) 15 529-664
  • [9] Choi J.(1974)Die Beugungserscheinungen einer kreisrunden Öffnung und eines kreisrunden Schirmchens theoretisch und experimentell bearbeitet J. Approx. Theory 5 41-65
  • [10] Rathie A. K.(1947)Die Beugungserscheinungen geradlinig begrenzter Schirme Trans. Amer. Math. Soc. 61 36-53
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