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

1986 ◽  
Vol 31 (1) ◽  
pp. 173-183 ◽  
Author(s):  
H. Haruki
Keyword(s):  
Functional Equation ◽  
Gamma Function

A Simple Characterization of the Gamma Function

1987 ◽  
Vol 94 (6) ◽  
pp. 534-536 ◽  
Author(s):  
Detlef Laugwitz ◽  
Bernd Rodewald
Keyword(s):  
Gamma Function ◽  
Simple Characterization

scholarly journals A note on a functional equation

1973 ◽  
Vol 15 (4) ◽  
pp. 385-388
Author(s):  
Chung-Ming An
Keyword(s):  
Functional Equation ◽  
Dirichlet Series ◽  
Gamma Function ◽  
Generalized Gamma ◽  
Special Cases ◽  
Generalized Gamma Function

The object of this note is to give an aspect to the problem of the functional equation of the generalized gamma function and Dirichlet series which are defined in [1]. In general, we cannot answer the problem yet. But it is worthy to attack this problem for some special cases.

scholarly journals Some results concerning the Cauchy functional equation in certain Banach algebras

1985 ◽  
Vol 31 (1) ◽  
pp. 137-144 ◽  
Author(s):  
J. Vukman
Keyword(s):  
Functional Equation ◽  
Hilbert Space ◽  
Identity Element ◽  
Banach Algebras ◽  
Cauchy Functional Equation

In this paper some results concerning the Cauchy functional equation, that is the functional equation f(x+y) = f(x) + f(y) in complex hermitian Banach *-algebras with an identity element are presented. As an application a generalization of Kurepa's extension of the Jordan-Neumann characterization of pre-Hilbert space is obtained.

Lifetime regression models based on a functional equation of physical nature

1987 ◽  
Vol 24 (01) ◽  
pp. 160-169 ◽  
Author(s):  
Enrique Castillo ◽  
Janos Galambos
Keyword(s):  
Functional Equation ◽  
Conditional Distribution ◽  
Regression Models ◽  
Practical Problem ◽  
Ad Hoc ◽  
Physical Nature ◽  
Value Theory ◽  
Complete Characterization ◽  
Lifetime Data

There are a number of ad hoc regression models for the statistical analysis of lifetime data, but only a few examples exist in which physical considerations are used to characterize the model. In the present paper a complete characterization of a regression model is given by solving a functional equation recurring in the literature for the case of a fatigue problem. The result is that, if the lifetime for given values of the regressor variable and the regressor variable for a given lifetime are both Weibull variables (assumptions which are well founded, at least as approximations, from extreme-value theory in some concrete applications), there are only three families of (conditional) distribution for the lifetime (or for the regressor variable). This model is then applied to a practical problem for illustration.

scholarly journals On the general solution of a functional equation connected to sum form information measures on open domain—III

1986 ◽  
Vol 9 (3) ◽  
pp. 545-550 ◽  
Author(s):  
Pl. Kannappan ◽  
P. K. Sahoo
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Open Domain ◽  
Information Measures ◽  
Domain Iii ◽  
Weighted Entropy ◽  
Form Information

In this series, this paper is devoted to the study of a functional equation connected with the characterization of weighted entropy and weighted entropy of degreeβ. Here, we find the general solution of the functional equation (2) on an open domain, without using0-probability and1-probability.

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