Euler's Beta function diagonalized and a related functional equation
Euler's Gamma function is the unique logarithmically convex solution of the functional equation \[\varphi(x+1)=x\varphi(x),\quad x\in\mathbb{R}_{+};\quad \varphi(1)=1,\] cf. the Proposition. In this paper we deal with the function \(\beta :\mathbb{R}_{+}\to\mathbb{R}_{+}\), \(\beta (x):=B(x,x)\...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AGH Univeristy of Science and Technology Press
2004-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol24/1/art/opuscula_math_2403.pdf |