Extended hypergeometric functions of two and three variables
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초록
Extensions of some classical special functions, for example, Beta function $B(x,y)$ and generalized hypergeometric functions $_{p}F_{q}$ have been actively investigated and found diverse applications. In recent years, several extensions for $B(x,y)$ and $_{p}F_{q}$ have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function $B_{p}^{\left(\alpha ,\beta; m \right)} \left(x,y\right)$. Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.
Abstract
Extensions of some classical special functions, for example, Beta function $B(x,y)$ and generalized hypergeometric functions $_{p}F_{q}$ have been actively investigated and found diverse applications. In recent years, several extensions for $B(x,y)$ and $_{p}F_{q}$ have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function $B_{p}^{\left(\alpha ,\beta; m \right)} \left(x,y\right)$. Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.
참고문헌 (10)
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