Fractional Integration and differentiation of the $(p, q)$-extended Bessel function
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We aim to present some formulas for Saigo hypergeometric fractional integral and differential operators involving $(p, q)$-extended Bessel function $J_{\nu,\,p,q} (z)$, which are expressed in terms of Hadamard product of the $(p, q)$-extended Gauss hypergeometric function and the Fox-Wright function $_{p}\Psi_{q}(z)$. A number of interesting special cases of our main results are also considered. Further, it is emphasized that the results presented here, which are seemingly complicated series, can reveal their involved properties via those of the two known functions in their respective Hadamard product.
Abstract
We aim to present some formulas for Saigo hypergeometric fractional integral and differential operators involving $(p, q)$-extended Bessel function $J_{\nu,\,p,q} (z)$, which are expressed in terms of Hadamard product of the $(p, q)$-extended Gauss hypergeometric function and the Fox-Wright function $_{p}\Psi_{q}(z)$. A number of interesting special cases of our main results are also considered. Further, it is emphasized that the results presented here, which are seemingly complicated series, can reveal their involved properties via those of the two known functions in their respective Hadamard product.
참고문헌 (26)
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