The aim of this work is to find "good" approximations to the Digamma function Ξ¨ . We construct an infinite family of "basic" functions {I a , a β [0, 1]} covering the Digamma function. These functions are shown to approximate Ξ¨ locally and asymptotically, and it is shown that for any x β R + , there
New approximations of the gamma function in terms of the digamma function
β Scribed by Cristinel Mortici
- Book ID
- 108052501
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 296 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0893-9659
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π SIMILAR VOLUMES
This routine occasionally gives wrong results, a correction GAMMA as part of their program for calculating the has been published in Computer Phys. Commun. 3 (1972) 276. Coulomb phase shift. We note here that Luke [13] has \* An earlier version of this program was written by ginary part. This can be
Let Ο(x) denote the digamma function, that is, the logarithmic derivative of Euler's -function. Let q be a positive integer greater than 1 and Ξ³ denote Euler's constant. We show that all the numbers Ο(a/q) + Ξ³, (a, q) = 1, 1 a q, are transcendental. We also prove that at most one of the numbers Ξ³, Ο