• 대한수학회논문집
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• 제33권1호
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• pp.143-155
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• 2018

In this present paper, our aim is to introduce an extended Wright-Bessel function $J^{{\lambda},{\gamma},c}_{{\alpha},q}(z)$ which is established with the help of the extended beta function. Also, we investigate certain integral transforms and generalized integration formulas for the newly defined extended Wright-Bessel function $J^{{\lambda},{\gamma},c}_{{\alpha},q}(z)$ and the obtained results are expressed in terms of Fox-Wright function. Some interesting special cases involving an extended Mittag-Leffler functions are deduced.

• 호남수학학술지
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• 제43권2호
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• pp.167-181
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• 2021

In this paper, the Saigo's k-fractional integral and derivative operators involving k-hypergeometric function in the kernel are applied to the generalized k-Bessel function; results are expressed in term of k-Wright function, which are used to present image formulas of integral transforms including beta transform. Also special cases related to fractional calculus operators and Bessel functions are considered.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.717-723
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• 2021

The purpose of the present paper is to give sufficient conditions for normalized Dini function which is the special combination of the generalized Bessel function of first kind to be in the classes k-starlike functions and k-uniformly convex functions.

• 대한수학회지
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• 제39권5호
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• pp.681-692
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• 2002

In the article [2], the conjugate Darboux-Protter problem Dn is formulated for the two dimensional wave equation in the class of unbounded functions and the uniqueness of solutions has been established. In this paper, we shall show the existence of solutions for the hyperbolic equations with Bessel operators in another special case.

• 호남수학학술지
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• 제41권1호
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• pp.101-116
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• 2019

In this paper our aim is to establish some geometric properties (like starlikeness, convexity and close-to-convexity) for the generalized and normalized Dini functions. In order to prove our main results, we use some inequalities for ratio of these functions in normalized form and classical result of Fejer.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권2호
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• pp.141-145
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• 2014

In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function ${\psi}^{\prime}(t)$ on (0, ${\infty}$).

• 한국소음진동공학회논문집
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• 제17권10호
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• pp.946-949
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• 2007

This paper discusses the lateral vibration of a beam with boundary condition of one end fixed and the other end free. The uniform beam has a solution by summation of some simple exponential functions. But if its shape is not uniform, its solution could be by Bessel's function or mathematical solution could not exist. Even if the solution of Bessel's function exists, as Bessel function is a series function, we must get the solution by numerical method. Author had proposed the solution of the matrix method by Ritz's method and a new mode shape function, and had earned the good results for a wedge beam. Hereby a vibration analysis for the tapered beam with circle cross section was executed, and so good results were showed.

• 대한수학회보
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• 제55권2호
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• pp.599-610
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• 2018

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.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.397-409
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• 2018

The aim of this research note is to evaluate two generalized integrals involving the product of generalized Bessel function and Jacobi polynomial by employing the result of Obhettinger [2]. Also, by mean of the main results, we have established an interesting relation in between $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ and Srivastava and Daoust functions. Some interesting special cases of our main results are also indicated.

• 대한수학회지
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• 제46권6호
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• pp.1277-1292
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• 2009

This paper is an attempt to stress the usefulness of the multivariable special functions. In this paper, we derive generating relations involving 3-variable 2-parameter Tricomi functions by using Lie-algebraic techniques. Further we derive certain new and known generating relations involving other forms of Tricomi and Bessel functions as applications.