• 대한수학회논문집
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• 제33권2호
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• pp.423-436
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• 2018

We aim to establish certain Saigo hypergeometric fractional integral formulas for a finite product of the generalized k-Bessel functions, which are also used to present image formulas of several integral transforms including beta transform, Laplace transform, and Whittaker transform. The results presented here are potentially useful, and, being very general, can yield a large number of special cases, only two of which are explicitly demonstrated.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.347-354
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• 2010

Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113~119] introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_oF_1$, $_1F_1$, a Humbert function ${\Psi}_2$, a Humbert function ${\Phi}_2$. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function $X_2$ among his twenty $X_i$ (i = 1, ..., 20), whose kernels include the Exton function $X_2$ itself, the Appell function $F_4$, and the Lauricella function $F_C$.

• 대한수학회논문집
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• 제27권2호
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• pp.257-264
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• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집B
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• pp.540-545
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• 2001

In this paper dynamic responses of an engine, which is supported by hydraulic mount, to throttle tip-in/tip out are analyzed. Because the hydraulic mounts have non-linearity which the characteristics of stiffness and damping vary with frequencies, it is difficult to analyze the dynamic behavior of an engine using general integral algorithms. Convolution integrals and relationships between unit impulse response functions and frequency response functions are therefore used to simulate the transient behavior of an engine indirectly. In time domain, impulse response functions are calculated by two-side discrete inverse Fourier transform of frequency response function achieved by Laplace transform of equations of motion. Considering the fact that the shapes of behavior of an engine simulated by the proposed method are in good agreement with test results, it is confirmed that the proposed method is very effective for the analysis of transient response to throttle tip-in/out of an engine with hydraulic mounts.