• 호남수학학술지
• /
• 제35권4호
• /
• pp.667-677
• /
• 2013

A remarkably large number of integrals involving a product of certain combinations of Bessel functions of several kinds as well as Bessel functions, themselves, have been investigated by many authors. Motivated the works of both Garg and Mittal and Ali, very recently, Choi and Agarwal gave two interesting unified integrals involving the Bessel function of the first kind $J_{\nu}(z)$. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present two generalized integral formulas involving a product of Bessel functions of the first kind, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. Some interesting special cases and (potential) usefulness of our main results are also considered and remarked, respectively.

• 호남수학학술지
• /
• 제40권1호
• /
• pp.61-73
• /
• 2018

The main aim of this research paper is to evaluate the general integral of the form $${\int_{0}^{1}}x^{c-1}(1-x)^{c+{\ell}}[1+{\alpha}x+{\beta}(1-x)]^{-2c-{\ell}-1}\atop {\times}_3F_2\left\[ {a,\;b,\;2c+{\ell}+1} \\ {\frac{1}{2}(a+b+i+1),\;2c+j\;;\frac{(1+{\alpha})x}{1+{\alpha}x+{\beta}(1-x)} }\right]dx$$ in the most general form for any ${\ell}{\in}\mathbb{Z}$; and $i, j=0,{\pm}1,{\pm}2$. The results are established with the help of generalized Watson's summation theorem due to Lavoie, et al. Fifty interesting general integrals have also been obtained as special cases of our main findings.

• Korean Journal of Mathematics
• /
• 제23권1호
• /
• pp.47-64
• /
• 2015

We express generalized Fourier-Feynman transform and convolution product of functionals in a Banach algebra $\mathcal{S}(L^2_{a,b}[0,T])$ as limits of function space integrals on $C_{a,b}[0,T]$. Moreover we obtain change of scale formulas for function space integrals related with generalized Fourier-Feynman transform and convolution product of these functionals.

• East Asian mathematical journal
• /
• 제14권1호
• /
• pp.63-76
• /
• 1998

we consider the hp-version to solve non-constant coefficients elliptic equations $-div(a{\nabla}u)=f$ with Dirichlet boundary conditions on a bounded polygonal domain $\Omega$ in $R^2$. In [6], M. Suri obtained an optimal error-estimate for the hp-version: ${\parallel}u-u^h_p{\parallel}_{1,\Omega}{\leq}Cp^{(\sigma-1)}h^{min(p,\sigma-1)}{\parallel}u{\parallel}_{\sigma,\Omega}$. This optimal result follows under the assumption that all integrations are performed exactly. In practice, the integrals are seldom computed exactly. The numerical quadrature rule scheme is needed to compute the integrals in the variational formulation of the discrete problem. In this paper we consider a family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties, which can be used for calculating the integrals. Under the numerical quadrature rules we will give the variational form of our non-constant coefficients elliptic problem and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.

• 대한수학회논문집
• /
• 제33권4호
• /
• pp.1285-1301
• /
• 2018

This paper is devoted to the study of $Tur{\acute{a}}n$-type inequalities for some well-known special functions such as Gauss hypergeometric functions, generalized complete elliptic integrals and confluent hypergeometric functions which are derived by using a new form of the Cauchy-Bunyakovsky-Schwarz inequality. We also apply these inequalities for some sample of interest such as incomplete beta function, incomplete gamma function, elliptic integrals and modified Bessel functions to obtain their corresponding $Tur{\acute{a}}n$-type inequalities.

• Kyungpook Mathematical Journal
• /
• 제48권2호
• /
• pp.165-171
• /
• 2008

The aim of this paper is to evaluate four finite integrals involving the product of Srivastava's polynomials, a generalized hypergeometric function and $\bar{H}$-function proposed by Inayat Hussian which contains a certain class of Feynman integrals. At the end, we give an application of our main findings by connecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electric networks, probability theory and statistical mechanics.

• 한국지능시스템학회논문지
• /
• 제14권1호
• /
• pp.33-38
• /
• 2004

이 논문에서는 Schmeidler[14]와 Narukawa[12]에 나오는 보단조 가법 실수치 범함수 개념의 일반화인 보단조 가법 구간치 범함수를 정의하고 그들의 성질을 연구한다. 또한 보단조 가법 구간치 범함수와 구간치 쇼케이적분이 적당한 함수공간 상에서 서로간의 관계를 조사한다. 수의 값을 갖는 함수들의 쇼케이적분을 생각하고자 한다. 이러한 구간 수의 값을 갖는 함수들의 성질들을 조사한다.

• 한국지능시스템학회논문지
• /
• 제17권4호
• /
• pp.451-454
• /
• 2007

Non-additive measures and their corresponding Choquet integrals are very useful tools which are used in both insurance and financial markets. In both markets, it is important to update prices to account for additional information. The update price is represented by the Choquet integral with respect to the conditioned non-additive measure. In this paper, we consider a price functional H on interval-valued risks defined by interval-valued Choquet integral with respect to a non-additive measure. In particular, we prove that if an interval-valued pricing functional H satisfies the properties of monotonicity, comonotonic additivity, and continuity, then there exists an two non-additive measures ${\mu}1,\;{\mu}2$ such that it is represented by interval-valued choquet integral on interval-valued risks.

• Kyungpook Mathematical Journal
• /
• 제56권2호
• /
• pp.465-471
• /
• 2016

In this paper, we establish certain integrals involving Srivastava's Polynomials [5] and Aleph Function ([8], [10]). On account of general nature of the functions and polynomials involved in the integrals, our results provide interesting unifications and generalizations of a large number of new and known results, which may find useful applications in the field of science and engineering. To illustrate, we have recorded some special cases of our main results which are also sufficiently general and unified in nature and are of interest in themselves.

• 호남수학학술지
• /
• 제41권1호
• /
• pp.163-174
• /
• 2019

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.