• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.67-79
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• 2018

In this paper, we present new generalized incomplete Pochhammer symbols and using this we introduce the extended generalized incomplete hypergeometric functions. We derive certain properties, generating functions and reduction formulas of these extended generalized incomplete hypergeometric functions. Special cases of this extended generalized incomplete hypergeometric functions are also discussed.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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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.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.285-288
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• 1998

A least-squares identification method is studied that estimates a finite number of coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions, We will expand and generalize the orthogonal functions as basis functions for dynamical system representations. To this end, use is made of balanced realizations as inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. We show that the Laplace transform of the expansion for some sets$\Psi_{\kappa}(Z)$ is equivalent to a series expansion . Techniques based on this result are presented for obtaining the coefficients $c_{n}$ as those of a series. One of their important properties is that, if chosen properly, they can substantially increase the speed of convergence of the series expansion. This leads to accurate approximate models with only a few coefficients to be estimated. The set of Kautz functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.889-900
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• 2005

We consider the second order mock theta functions defined by McIntosh and define generalized functions. We give integral representation and multibasic expansion of these functions. We also show that they are $F_q$-functions.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.97-108
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• 2014

In the theory of special functions, it is important to study some formulae describing hypergeometric functions with other hypergeometric functions. In this paper, we give some methods to obtain a lot of decomposition formulae for generalized hypergeometric functions.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.221-233
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• 2004

In this paper we introduce the concept of the McShane-Stieltjes integrals of interval-valued functions and fuzzy-number-valued functions and investigate some of their properties.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.107-122
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• 2009

In this paper, we deal with the problem of uniqueness of meromorphic functions that share three values, and obtain some theorems which improve some results of Brosch, Yi and other authors.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.117-129
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• 2005

We give a generalization of bilateral mock theta functions of order eight and show that they are $F_q$-functions. We also give an integral representation for these functions. We give a relation between mock theta functions of the first set and bilateral mock theta functions of the second set.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.241-248
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• 2005

Some of the generalized continuous functions and their basic properties are introduced in concern with the cover theory. The open property of a function is a crucial tool for the survey of this area.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1239-1248
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• 2018

Recently, many authors have obtained several hypergeometric identities involving hypergeometric functions of one and multi-variables such as the Appell's functions and Horn's functions. In this paper, we obtain several new transformations suitably by applying the fractional calculus operator to these hypergeometric identities, which was introduced recently by Tremblay.