Difference between revisions of "Digamma"

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=See Also=
 
=See Also=
[[Gamma function]] <br />
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[[Gamma]] <br />
 
[[Polygamma]]<br />
 
[[Polygamma]]<br />
 
[[Trigamma]] <br />
 
[[Trigamma]] <br />
  
 
=References=
 
=References=
* {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=findme|next=findme}}: $\S 1.7 (1)$
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* {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=findme|next=findme}}: $\S 1.7 (1)$
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Beta is symmetric|next=Digamma at 1}}: $6.3.1$
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Beta is symmetric|next=Digamma at 1}}: $6.3.1$
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 23:21, 3 March 2018

The digamma function $\psi \colon \mathbb{C} \setminus \{0,-1,-2,\ldots\} \rightarrow \mathbb{C}$ is defined by $$\psi(z) = \dfrac{\mathrm{d}}{\mathrm{d}z} \log \Gamma(z) = \dfrac{\Gamma'(z)}{\Gamma(z)}.$$

Properties

Partial derivative of beta function
Digamma at 1
Digamma functional equation
Digamma at n+1

See Also

Gamma
Polygamma
Trigamma

References