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[en] Generalized hypergeometric functions include, as particular cases, many special functions occurring in nuclear sciences (for example Bessel functions and incomplete γ-functions). Owing to their various properties, hypergeometric functions have found a large number of applications in fields such as atmospheric radionuclide releases, heat transfer, statistical distributions and hydrodynamics. Their representations entail parameters that are written in the form (a)n, which is known as Pochhammer's symbol. When transforming higher order hypergeometric functions to ones of lower orders and in other operations, one often encounters particular difficulties due to the fact that there may be no trivial relations between compound parameters of the Pochhammer kind. For example, one may be faced with breaking up the product (a+b)n. The result presented here helps to overcome this particular problem. (author)
[en] The aim of this research paper is to establish a quite general transformation involving hypergeometric functions by the method of elementary manipulation of the series representations. Certain known, as well as new hypergeometric transformations and identities not previously recorded in the literature, are then deduced by means of the generalized Kummer and Dixon theorems obtained earlier by Lavoie et al. An application of a newly obtained identity is also given
[en] The purpose of present work is to investigate three definite integrals, concerning the generalized hypergeometric function together with the general class of Srivastava’s polynomials. Our theorems will reduces in known results for a particular values of parameters.
[en] Simple inequalities for some integrals involving the modified Struve function of the first kind are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality, involving the modified Struve function , for a generalized hypergeometric function.
[en] We present a generalization of a compact form, due to Baker, for quadratic identities satisfied by the three-index p-functions on curves of genus g=2, and a further generalization of a new result in genus g=3. The compact forms involve a bordered determinant containing 2(g-1)(g+1) free parameters. -- Highlights: → Properties of Weierstrass P-functions for hyperelliptic curves. → Generalization of result of H.F. Baker for genus two case. → Compact formulae with maximal number of parameters in genus two and three cases.
[en] The purpose of this article is to give a theorem of the linear degeneration for meromorphic mappings of Cm into CPn with (2n+2) hyperplanes and multiplicities are truncated by (n+1). (author)
[en] Even positive-definite splines with support in [-1,1] that are equal to real algebraic polynomials on [0,1] are investigated. Examples of such splines are presented. Under consideration are the e-splines, which have several extremal properties, and the positive-definite A-splines, which have the maximum possible smoothness on R. An estimate of the approximation by a linear combination of shifts of an A-spline is indicated. New relations for the hypergeometric function 1F2 are found