The Journal of the Indian Mathematical Society

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A New Class of Functions Suggested by the Generalized Basic Hypergeometric Function


Affiliations
1 Department of Mathematics, The Maharaja Sayajirao University of Baroda,Vadodara-390 002, India
2 Department of Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara-390 002, India
     

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We introduce an extended generalized basic hypergeometric function rΦs+p in which p tends to infinity together with the summation index. We define the difference operators and obtain infinite order difference equation, for which these new special functions are eigen functions. We derive some properties, as the order zero of this function, differential equation involving a particular hyper-Bessel type operators of infinite order, and contiguous function relations. A transformation formula and an l-analogue of the q-Maclaurin's series are also obtained.

Keywords

Basic Hypergeometric Function, q-Derivative, q-Integral, Eigen Function, Infinite Order Difference Equation.
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Abstract Views: 354

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  • A New Class of Functions Suggested by the Generalized Basic Hypergeometric Function

Abstract Views: 354  |  PDF Views: 1

Authors

Meera H. Chudasama
Department of Mathematics, The Maharaja Sayajirao University of Baroda,Vadodara-390 002, India
B. I. Dave
Department of Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara-390 002, India

Abstract


We introduce an extended generalized basic hypergeometric function rΦs+p in which p tends to infinity together with the summation index. We define the difference operators and obtain infinite order difference equation, for which these new special functions are eigen functions. We derive some properties, as the order zero of this function, differential equation involving a particular hyper-Bessel type operators of infinite order, and contiguous function relations. A transformation formula and an l-analogue of the q-Maclaurin's series are also obtained.

Keywords


Basic Hypergeometric Function, q-Derivative, q-Integral, Eigen Function, Infinite Order Difference Equation.

References