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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.
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참고문헌 (26)
참고문헌 신청
M. A. Chaudhry / 1997 / Extension of Euler's beta function / J. Comput. Appl. Math. 78(1):19~32
M. A. Chaudhry / 2004 / Extended hypergeometric and confluent hypergeometric functions / Appl. Math. Comput. 159(2):589~602
M. A. Chaudhry / 2002 / On a Class of Incomplete Gamma Functions with Applications / Chapman & Hall/CRC
최준상 / 2017 / Mathieu-type series built by (p, q)-extended Gaussian hypergeometric function / 대한수학회보 54(3):789~797
최준상 / 2014 / EXTENSION OF EXTENDED BETA, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS / 호남수학학술지 36(2):357~385
M. A. Chaudhry / 2004 / Extended hypergeometric and confluent hypergeometric functions / Appl. Math. Comput. 159(2):589~602
M. A. Chaudhry / 2002 / On a Class of Incomplete Gamma Functions with Applications / Chapman & Hall/CRC
최준상 / 2017 / Mathieu-type series built by (p, q)-extended Gaussian hypergeometric function / 대한수학회보 54(3):789~797
최준상 / 2014 / EXTENSION OF EXTENDED BETA, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS / 호남수학학술지 36(2):357~385
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