CERTAIN EXTENDED SPECIAL FUNCTIONS AND FRACTIONAL INTEGRAL AND DERIVATIVE OPERATORS VIA AN EXTENDED BETA FUNCTION
CERTAIN EXTENDED SPECIAL FUNCTIONS AND FRACTIONAL INTEGRAL AND DERIVATIVE OPERATORS VIA AN EXTENDED BETA FUNCTION
Rahman Gauhar(International Islamic University); Mubeen Shahid(University of Sargodha); Nisar Kottakkaran Sooppy(Prince Sattam bin Abdulaziz University); Choi Junesang(Dongguk University)
24권 1호, 1~13쪽
초록
Various extensions of the Euler’s beta function have, recently, been presented and investigated. Here, choosing to use a fully extended beta function, we introduce an extended hypergeometric function, an extended confluent hypergeometric function, and an extension of the Appell function F1. We, also, use the fully extended beta function to introduce an extended Riemann-Liouville type integral operator and investigate its associated formulas and generating relations. The results presented here, being very general, can be specialized to yield some known and new results.
Abstract
Various extensions of the Euler’s beta function have, recently, been presented and investigated. Here, choosing to use a fully extended beta function, we introduce an extended hypergeometric function, an extended confluent hypergeometric function, and an extension of the Appell function F1. We, also, use the fully extended beta function to introduce an extended Riemann-Liouville type integral operator and investigate its associated formulas and generating relations. The results presented here, being very general, can be specialized to yield some known and new results.
- 발행기관:
- 경남대학교 수학교육과
- 분류:
- 수학일반