A new characterization of euler's gamma function by a functional equation

This paper gives a new characterization of Euler's gamma function from the aspect of complex analysis. To this end the Gauss multiplication formula is used.     

含有快速增长非线性恢复力的梁方程的行波解

Abstract. On studying traveling waves on a nonlinearly suspended bridge,the following partial differential equation has been considered:     

Holomorphic solutions of an inhomogeneous Cauchy equation

Summary We consider the functional equation(x + y) – (x) – (y) = f(x)f(y)h(x + y) and we find all its homomorphic solutionsf, h, defined in a neighbourhood of the origin.     

The entire solutions of a polynomial difference equation

Recently S. Shimomura has shown that the polynomial difference equationw(z + 1) =P(w(z)), whereP is a given polynomial of degree at least two, always has entire non-constant solutions. The present investigation shows how to construct all entire solutions of the equation and discusses some properties of the solutions.     

Theq-gamma function forx<0

F. H. Jackson defined aq analogue of the gamma function which extends theq-factorial (n!) _q =1(1+q)(1+q+q ²)...(1+q+q ²+...+q ^n–1) to positivex. Askey studied this function and obtained analogues of most of the classical facts about the gamma function, for 0<q<1. He proved an analogue of the Bohr-Mollerup theorem, which states that a logarithmically convex function satisfyingf(1)=1 andf(x+1)=[(q ^x –1)/(q–1)]f(x) is in fact theq-gamma function He also studied the behavior of _q asq changes and showed that asq1^–, theq-gamma function becomes the ordinary gamma function forx>0.I proved many of these results forq>1. The current paper contains a study of the behavior of _q (x) forx<0 and allq>0. In addition to some basic properties of _q , we will study the behavior of the sequence {x _n (q)} of critical points asn orq changes.     

On a functional equation for Jacobi's elliptic function cn(z; k)

The purpose of this paper is to give a characterization of Jacobi's elliptic function cn(z; k) by use of a functional equation which is a generalization of the cosine functional equation.     

On approximate solutions of the Pexider equation

Summary LetX be an abelian (topological) group andY a normed space. In this paper the following functional inequality is considered: {ie143-1} This inequality is a similar generalization of the Pexider equation as J. Tabor's generalization of the Cauchy equation (cf. [3], [4]). The solutions of our inequality have similar properties as the solutions of the Pexider equation. Continuity and related properties of the solutions are investigated as well.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth.