Difference between revisions of "Digamma"
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Revision as of 03:11, 21 December 2016
The digamma function $\psi \colon \mathbb{C} \setminus \{0,-1,-2,\ldots\} \rightarrow \mathbb{C}$ is defined by $$\psi(z) = \dfrac{\mathrm{d}}{\mathrm{d}z} \log \Gamma(z) = \dfrac{\Gamma'(z)}{\Gamma(z)}.$$
Graph of $\psi$.
Domain coloring of $\psi(z)$.
Properties
Partial derivative of beta function
Digamma at 1
Digamma functional equation
Digamma at n+1
See Also
Gamma function
Polygamma
Trigamma
References
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.7 (1)$
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $6.3.1$
