• 대한수학회논문집
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• 제32권1호
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• pp.75-84
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• 2017

In recent years, several interesting families of generating functions for various classes of hypergeometric functions were investigated systematically. In the present paper, we introduce a new family of extended Wright type hypergeometric function and obtain several classes of generating relations for this extended Wright type hypergeometric function.

• East Asian mathematical journal
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• 제21권2호
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• pp.191-203
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• 2005

In the present paper we first establish some basic results for a substantially more general class of functions defined below. The results include simple differentiation and fractional calculus operators(integration and differentiation of arbitrary orders) for this class of functions. These results are then invoked in determining similar properties for the generalized Wright's hypergeometric functions. Further, norm estimate of a certain class of integral operators whose kernel involves the generalized Wright's hypergeometric function, and its composition(and other related properties) with the fractional calculus operators are also investigated.

• 대한수학회논문집
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• 제34권1호
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• pp.203-211
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• 2019

In this note, new sharpened Redheffer type inequalities related to the Fox-Wright functions are established. As consequence, we show new Redheffer type inequalities for hypergeometric functions and for the four-parametric Mittag-Leffler functions with best possible exponents.

• 호남수학학술지
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• 제41권1호
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• pp.163-174
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• 2019

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.

• 대한수학회논문집
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• 제32권1호
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• pp.47-53
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• 2017

Generalized integral formulas involving the generalized modified k-Bessel function $J^{b,c,{\gamma},{\lambda}}_{k,{\upsilon}}(z)$ of first kind are expressed in terms generalized Wright functions. Some interesting special cases of the main results are also discussed.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.99-111
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• 2024

In this paper, a new seven-parameter Mittag-Leffler function of a single complex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

• 대한수학회논문집
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• 제34권2호
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• pp.523-532
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• 2019

Integrals involving a finite product of the generalized Bessel functions have recently been studied by Choi et al. [2, 3]. Motivated by these results, we establish certain unified integral formulas involving a finite product of the generalized k-Bessel functions. Also, we consider some integral formulas of the (p, q)-extended Bessel functions $J_{{\nu},p,q}(z)$ and the Delerue hyper-Bessel function which are proved in terms of (p, q)-extended generalized hypergeometric functions, and the generalized Wright hypergeometric functions, respectively.

• 대한수학회논문집
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• 제32권3호
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• pp.677-688
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• 2017

The composition of Jacobi type finite classes of the classical orthogonal polynomials with two generalized Riemann-Liouville fractional derivatives are considered. The outcomes are expressed in terms of generalized Wright function or generalized hypergeometric function. Similar composition formulas are also obtained by considering the generalized Riemann-Liouville and $Erd{\acute{e}}yi-Kober$ fractional integral operators.

• 대한수학회보
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• 제51권4호
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• pp.995-1003
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• 2014

A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas involving various Bessel functions have been presented. Very recently, Choi and Agarwal derived two generalized integral formulas associated with the Bessel function $J_{\nu}(z)$ of the first kind, which are expressed in terms of the generalized (Wright) hypergeometric functions. In the present sequel to Choi and Agarwal's work, here, in this paper, we establish two new integral formulas involving the generalized Bessel functions, which are also expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.249-255
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• 2016

The object of the present paper is to establish two interesting unified integral formulas involving Multiple (multiindex) Mittag-Leffler functions, which is expressed in terms of Wright hypergeometric function. Some deduction from these results are also considered.