R. G. Buschman
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View article: Rreducible H-functions of two variables
Rreducible H-functions of two variables Open
A reduction formula for certain H-funtions of two variables to H-functions of one variable is obtained. A special case is the known reduction formula for Appell's funcrions F2 the Gauss function 2F1.
View article: Finite Laplace transformation
Finite Laplace transformation Open
Over the years several authors have obtained various properties of the Laplace transformation with the integration restricted to a finite interval. We discuss the operational properties and illustrate their applications to a boundary value…
View article: Theory of the General $H$-function of Two Variables
Theory of the General $H$-function of Two Variables Open
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View article: Heat transfer between a fluid and a plate: multidimensional Laplace transformation methods
Heat transfer between a fluid and a plate: multidimensional Laplace transformation methods Open
Multidimensional Laplace transformations are used to obtain the surface temperature and the surface heat flux of a plate with a fluid flowing across it without solving the complete boundary value problem. It is also shown that the constant…
View article: Substitution relations for laplace transformations
Substitution relations for laplace transformations Open
Additional results are obtained which center around expressions for the Laplace transforms of functions of the form k ( t ) F [ g ( t )]. The finite Laplace transformation is involved in a number of the formulas. Examples involving several…
View article: Addendum to: “Some polynomials defined by generating relations” (Trans. Amer. Math. Soc. 205 (1975), 360–370)
Addendum to: “Some polynomials defined by generating relations” (Trans. Amer. Math. Soc. 205 (1975), 360–370) Open
Certain constraints are explicitly specified for the validity of a recent result involving a multivariate generating function, due to the present authors [1, p. 369, Theorem 6]. It is also indicated how this result can be further generaliz…
View article: Mellin convolutions and H -function transformations
Mellin convolutions and H -function transformations Open
An elegant expression is obtained for an Hfunction transform of the Mellin convolution of two functions in terms of the Mellin convolution of H-function transforms of the functions.This main result leads to several new and interesting rela…
View article: Inequalities for hypergeometric functions
Inequalities for hypergeometric functions Open
The upper and lower bounds for the determinant of a dominant diagonal matrix have been used recently to obtain bounds on the classical orthogonal polynomials. Similar methods are used here on the hypergeometric functions of Gauss and of Ku…
View article: Finite sum representations for partial derivatives of special functions with respect to parameters
Finite sum representations for partial derivatives of special functions with respect to parameters Open
The Mellin transformation is used as a method for discovery of cases where the partial derivatives with respect to parameters for certain Whittaker and Bessel functions can be expressed in terms of finite sums involving these functions. Th…
View article: Sieve-Generated Sequences with Translated Intervals
Sieve-Generated Sequences with Translated Intervals Open
Consider the following sieve process. Let A (1) be the sequence of integers greater than 1. Let A (n+1) be obtained from A (n) = {a 1 (n) , a 2 (n) , …} by eliminating one element from each of the intervals I k (n), where We let a n = a n …
View article: An integral transformation relation
An integral transformation relation Open
with I (X+ 1)ao(x-1)a'I as weight function. We call (x-ao)ao ** (x-a,)aJP still the weight function of the generalized Jacobi polynomials of the order p. By introduction of the extended Heine-Stieltjes polynomials p(ao 'aP)(x) = (x-ao)aO *…