Convexity in the Theory of the Gamma Function
Convexity in the Theory of the Gamma Function
复制标题
伽马函数理论中的凸性
DOI：
10.1007/978-3-0348-5563-1_7
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发表时间：
1978
影响因子：
4
通讯作者：
H. Kairies
中科院分区：
文献类型：
--
作者：
H. Kairies
与 Artin 对伽马函数的公理化处理类似，这里研究了 Γ:IR+ → IR+ 在多大程度上可以被表征为函数方程的适当组合的凸解
$$ f\left( {x + 1} \right) = xf\left( x \right),f\left( {\frac{x}{2}} \right)f\left( {\frac{{x + 1}}{2}} \right) = 2\sqrt \pi {2^{ - x}}f\left( x \right),f\left( x \right)f\left( {1 - x} \right) = \pi /\sin \pi x。 $$
In analogy with Artin’s axiomatic treatment of the gamma function, it is here investigated to what extent Γ:IR+ → IR+ can be characterized as a convex solution of suitable combinations of the functional equations
$$ f\left( {x + 1} \right) = xf\left( x \right),f\left( {\frac{x}{2}} \right)f\left( {\frac{{x + 1}}{2}} \right) = 2\sqrt \pi {2^{ - x}}f\left( x \right),f\left( x \right)f\left( {1 - x} \right) = \pi /\sin \pi x. $$