• Communications of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.169-183
• /
• 2019

The main aim of this paper is to establish a new class of integrals involving the generalized Galu$Galu{\grave{e}}$-type Struve function with the different type of polynomials such as Jacobi, Legendre, and Hermite. Also, we derive the integral formula involving Legendre, Wright generalized Bessel and generalized Hypergeometric functions. The results obtained here are general in nature and can deduce many known and new integral formulas involving the various type of polynomials.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.679-684
• /
• 2005

In this paper, we characterize a permutation property of a certain type of binomials over the field through the use of Hermite's criterion.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2008.10a
• /
• pp.375-394
• /
• 2008

This paper discusses two user-friendly reliability techniques that could be implemented easily using the ubiquitous EXCEL. The techniques are First-Order Reliability Method with non-Gaussian random variables expressed using Hermite polynomials and collocation-based stochastic response surface method. It is believed that ease of implementation would popularize use of reliability-based design in practice.

• Journal of the Korean Statistical Society
• /
• v.36 no.3
• /
• pp.411-421
• /
• 2007

The recent work by the authors (see, Withers, 1999; Withers and McGavin, 2006; Withers and Nadarajah, 2006) provided new expressions for repeated upper tail integrals of the univariate normal density and so also for the general Hermite function. Here we derive new expressions for repeated lower tail integrals of the same. The calculations involve the use of Moran's L-function and the Airy function. In particular, the Hermite functions are expressed in terms of Moran's L-function and vice versa.

• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.473-484
• /
• 2018

In this paper, we discuss how the operational calculus can be exploited to the theory of generalized special functions of many variables and many indices. We obtained the generating relations for 3-index, 3-variable and 1-parameter Hermite polynomials. Some mixed type generating relations and bilateral generating relations of many indices and many variable like Lagurre-Hermite and Hermite-Sister Celine's polynomials are also obtained. Further we generalize some results on old symbolic notations using operational identities.

• Communications of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.177-193
• /
• 2022

The main aim of this paper is to introduce a new generalization of the Wright series in two variables, which is expressed in terms of Hermite polynomials. The properties of the freshly defined function involving its auxiliary functions and the integral representations are established. Furthermore, a Gauss-Hermite quadrature and Gaussian quadrature formulas have been established to evaluate some integral representations of our main results and compare them with our theoretical evaluations using graphical simulations.

• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.973-1008
• /
• 1997

We reconsider the problem of calssifying all classical orthogonal polynomial sequences which are solutions to a second-order differential equation of the form $$ \ell_2(x)y"(x) + \ell_1(x)y'(x) = \lambda_n y(x). $$ We first obtain new (algebraic) necessary and sufficient conditions on the coefficients $\ell_1(x)$ and $\ell_2(x)$ for the above differential equation to have orthogonal polynomial solutions. Using this result, we then obtain a complete classification of all classical orthogonal polynomials : up to a real linear change of variable, there are the six distinct orthogonal polynomial sets of Jacobi, Bessel, Laguerre, Hermite, twisted Hermite, and twisted Jacobi.cobi.

• Journal of Environmental Science International
• /
• v.11 no.9
• /
• pp.907-914
• /
• 2002

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.

• Kyungpook Mathematical Journal
• /
• v.14 no.2
• /
• pp.171-184
• /
• 1974

• Communications of the Korean Mathematical Society
• /
• v.24 no.2
• /
• pp.171-180
• /
• 2009

In this paper, we give three criteria for non-polynomial functions interpolated from the set of univariate polynomials of degree less than m over a finite field to be a permutation on the same set.