A Family of the Incomplete Hypergeometric Functions and Associated Integral Transform and Fractional Derivative Formulas

作者：Srivastava Rekha^*; Agarwal Ritu; Jain Sonal

来源：Filomat, 2017, 31(1): 125-140.

DOI：10.2298/FIL1701125S

• Gamma and Beta functions
• Incomplete gamma functions
• Incomplete Pochhammer symbols
• Integral transforms
• Hypergeometric and incomplete hypergeometric functions
• Fractional derivative operators of the Riemann-Liouville
• the Weyl
• the Erdelyi-Kober and other types
• Kampe de Feriet function

Recently, Srivastava et al. [Integral Transforms Spec. Funct. 23 (2012), 659-683] introduced the incomplete Pochhammer symbols that led to a natural generalization and decomposition of a class of hypergeometric and other related functions as well as to certain potentially useful closed-form representations of definite and improper integrals of various special functions of applied mathematics and mathematical physics. In the present paper, our aim is to establish several formulas involving integral transforms and fractional derivatives of this family of incomplete hypergeometric functions. As corollaries and consequences, many interesting results are shown to follow from our main results.

• 出版日期2017