• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.235-245
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• 2006

Applications of Weyl fractional $q$-integral operator to various generalized basic hypergeometric functions including the basic analogue of Fox's H-function have been investigated in the present paper. Certain interesting special cases have also been deduced.

• 호남수학학술지
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• 제43권1호
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• pp.26-34
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• 2021

In this paper two interesting double integrals involving product of two generalized hypergeometric functions have been evaluated in terms of gamma function. The results are derived with the help of known integrals involving hypergeometric functions recorded in the paper of Rathie et al. [6]. We also give several very interesting special cases.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.731-752
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• 2020

We introduce the p-deformation of generalized Humbert polynomials. For these polynomials, we derive the differential equation, generating function relations, Fibonacci-type representations, and recurrence relations and state the companion matrix. These properties are illustrated for certain polynomials belonging to p-deformed generalized Humbert polynomials.

• 충청수학회지
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• 제23권1호
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• pp.37-48
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• 2010

In this paper we use a generalized Brownian motion process to defined an analytic operator-valued generalized Feynman integral. We then obtain explicit formulas for the analytic operatorvalued generalized Feynman integrals for functionals of the form $$F(x)=f\({\int}^T_0{\alpha}_1(t)dx(t),{\cdots},{\int}_0^T{\alpha}_n(t)dx(t)\)$$, where x is a continuous function on [0, T] and {${\alpha}_1,{\cdots},{\alpha}_n$} is an orthonormal set of functions from ($L^2_{a,b}[0,T]$, ${\parallel}{\cdot}{\parallel}_{a,b}$).

• 호남수학학술지
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• 제32권1호
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• pp.1-16
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• 2010

By using the generalized operator method given by Burchnall and Chaundy in 1940, the authors present one-dimensional inverse pairs of symbolic operators. Many operator identities involving these pairs of symbolic operators are rst constructed. By means of these operator identities, 11 decomposition formulas for the generalized hypergeometric $_4F_3$ function are then given. Furthermore, the integral representations associated with generalized hypergeometric functions are also presented.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.601-609
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• 2020

In this paper, we introduce degenerate generalized poly-Bernoulli numbers and polynomials with (p, q)-logarithm function. We find some identities that are concerned with the Stirling numbers of second kind and derive symmetric identities by using generalized falling factorial sum.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.121-136
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• 2021

In this paper we wish to prove some results relating to the growth rates of composite entire and meromorphic functions with their corresponding left and right factors on the basis of their generalized order (��, ��) and generalized lower order (��, ��), where �� and �� are continuous non-negative functions defined on (-∞, +∞).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권2호
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• pp.139-154
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• 2023

In this paper we wish to prove some results relating to the growth rates of composite entire and meromorphic functions with their corresponding left and right factors on the basis of their generalized relative order (α, β) and generalized relative lower order (α, β), where α and β are continuous non-negative functions defined on (-∞, +∞).

• 대한수학회논문집
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• 제29권3호
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• pp.479-487
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• 2014

In this paper, we obtain some theorems on certain Euler type integrals involving generalized Mittag-Leffler function. Further, we deduce some special cases involving Wiman function, Prabhakar function and exponential and binomial functions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권2호
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• pp.141-155
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• 2011

We compute zeta functions of 1-solenoids. When our 1-solenoid is nonorientable, we compute Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid and its orientable double cover explicitly in terms of adjacency matrices and branch points. And we show that Artin-Mazur zeta function of orientable double cover is a rational function and a quotient of Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid.