• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1169-1177
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• 2016

This paper is devoted to the study of Mellin, Laplace, Euler and Whittaker transforms involving Struve function, generalized Wright function and Fox's H-function. The main results are presented in the form of four theorems. On account of the general nature of the functions involved here in, the main results obtained here yield a large number of known and new results in terms of simpler functions as their special cases. For the sake of illustration some corollaries have been recorded here as special cases of our main findings.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.393-400
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• 2017

Very recently, Srivastava et al. [8] introduced an extension of the Pochhammer symbol and used it to define a generalization of the generalized hypergeometric functions. In this paper, by using the generalized Pochhammer symbol, we extend the generalized Hurwitz-Lerch Zeta function by Goyal and Laddha [6] and investigate some interesting properties which include various integral representations, Mellin transforms, differential formula and generating function. Some interesting special cases of our main results are also considered.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.485-506
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• 2023

This paper investigates an extended form Hurwitz-Lerch zeta function, as well as related integral images, ordinary and fractional derivatives, and series expansions, using the term extended beta function. We establish a connection between the extended Hurwitz-Lerch zeta function and the Laguerre polynomials. Furthermore, we present a probability distribution application of the extended Hurwitz-Lerch zeta function ζ^𝛿,𝜇_𝜈,λ. Several results, both known and new, are shown to follow as special cases of our findings.

• Kyungpook Mathematical Journal
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• v.18 no.2
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• pp.211-215
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• 1978

In the present paper, we obtain two new and interesting finite summation formulae for the H-function of two variables in a very neat and elegant form. The novel feature of the paper is that the method used here in deriving these formulae is simple and direct and does not impose heavy restrictions on the parameters involved. On account of the most general nature of the H-function of two variables, a number of related finite summation formulae for a number of other useful functions can also be obtained as special cases of our results. As an illustration, we have obtained here from our main results, the corresponding finite summation formulae for $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function. Appell's function and Gauss' hypergeometric function which are also believed to be new.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.597-612
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• 2021

Several useful and interesting extensions of the various special functions have been introduced by many authors during the last few decades. Various integral formulas associated with Wright function have been studied and a noteworthy amount of work have found in literature. The principal object of the present paper is to evaluate finite integral formulas containing the product of orthogonal polynomials with generalized Wright function. These integral formulas are expressed in terms of Srivastava and Daoust function. Some interesting particular cases are obtained from the main results by specialising the suitable values of the parameters involved.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.681-692
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• 2022

Special functions and Geometric function theory are close related to each other due to the surprise use of hypergeometric function in the solution of the Bieberbach conjecture. The purpose of this paper is to provide a set of sufficient conditions under which the normalized four parametric Wright function has lower bounds for the ratios to its partial sums and as well as for their derivatives. The sufficient conditions are also obtained by using Alexander transform. The results of this paper are generalized and also improved the work of M. Din et al. [15]. Some examples are also discussed for the sake of better understanding of this article.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.29-38
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• 2017

The main objective of this paper is to establish certain unified integral formula involving the product of the generalized Mittag-Leffler type function $E^{({\gamma}_j),(l_j)}_{({\rho}_j),{\lambda}}[z_1,{\ldots},z_r]$ and the Srivastava's polynomials $S^m_n[x]$. We also show how the main result here is general by demonstrating some interesting special cases.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.549-560
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• 2018

Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.

• Proceedings of the Safety Management and Science Conference
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• 2010.11a
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• pp.551-557
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• 2010

The research proposes the hypergeometric, binomial and Poisson yield models for defective and defect. The paper also presents the hypothesis test, confidence interval and control charts for DPU(Defect Per Unit) and DPO(Defect Per Opportunity). Especially the study considers the analysis of compound Poisson yield models using various DOU density distributions.