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A strategy of eculizumab treatment withdrawal with disease monitoring is cost-effective compared to lifelong treatment for eligible atypical haemolytic uraemic syndrome patients: an economic evaluation of the SETS aHUS trial

Orozco-Leal G, Vale L, Oluboyede Y, Bryant A, Weetman C, Kennedy C, Kavanagh D, Wong E, Lecouturier J, Woodward L, Brocklebank V, Johnson S, Dunn S, Chadwick T, Sheerin NS.   +14 more
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Integral representations for the Gamma function, the Beta function, and the Double Gamma function

Integral Transforms and Special Functions, 2009
A variety of integral representations for some special functions have been developed. Here we aim at presenting certain (new or known) integral representations for , B(α, β), and by using some of the known integral representations of the Hurwitz (or generalized) Zeta function ζ(s, a).
Junesang Choi, Hari M. Srivastava
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Gamma Functions, Beta Functions, and Related

2021
Topics of this chapter are gamma functions, beta functions, and related functions in the complex domain. The evaluations are based on various numerical techniques in dependence of the function argument. Related functions are the Pochhammer symbol, the psi or digamma function, the incomplete gamma function and its first and second derivative, the ...
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Gamma, Beta, and Error Functions

2016
The gamma function, written as G(x), was first introduced by the mathematician Leonhard Euler (1707–1783) as a general form of the factorial function x! that could be applied to complex and negative numbers. Later, Adrien-Marie Legendre (1752–1833) who provided a “duplication formula” for the G function, introduced the notation that is commonly used ...
Vasudevan Lakshminarayanan, L. Srinivasa Varadharajan   +1 more
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Approximate gamma–beta type functions

Nonlinear Analysis: Theory, Methods & Applications, 2009
Abstract We show that every unbounded approximate gamma–beta type function is of gamma–beta type. That is, we obtain the superstability of a gamma–beta type functional equation β ( x , y ) f ( x + y ) = f ( x ) f ( y ) and also investigate the stability in the sense of R .
Gwang Hui Kim, Young Whan Lee
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Stability of generalized gamma and beta functional equations

Aequationes mathematicae, 2000
The aim of the paper is to prove stability results for the functional equation \[ f(x+p,y+q)=\varphi(x,y)f(x,y), \tag \(*\) \] where \(f:(0,\infty)\times (0,\infty) \to \mathbb R\), \(p,q\) are fixed positive numbers and \(\varphi:(0,\infty)\times (0,\infty) \to (0,\infty)\) is a suitable function. The main results are the following.
G. H. Kim, Y. W. Lee, Kil-Woung Jun
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Note on the Beta and Gamma Functions

The American Mathematical Monthly, 1969
In N. Bourbaki, IDlements de Mathematique, Fonctions d'une variable reelle, Ch. 1, 2, 3, 2me Md., 1958, p. 127, one finds a simple and interesting method of evaluating the Euler-Poisson integral f ex2dx without the use of double integrals or an inversion of limit operations.
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