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Polygamma function

In mathematics, the polygamma function of order m is a meromorphic function on the complex numbers C {\displaystyle \mathbb {C} } defined as the (m + 1)th derivative of the logarithm of the gamma function:

Recurrence relation, Series representation & Integral representation

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Overview

Integral representation

Recurrence relation

Multiplication theorem

Series representation

Taylor series

Asymptotic expansion

Inequalities

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Polygamma function

Nodes42
Edges41
Triples7
Avg. degree1.95
Density0.047619
Components1

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Polygamma function

Top relations

related to Integral representation · 3
Polygamma function → Hurwitz, Re, When
related to Series representation · 3
Polygamma function → Hurwitz, The, This
see also · 1
Polygamma function → FactorialGamma

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Important terminology

function polygamma displaystyle functions representation series gamma digamma mathbb theorem trigamma zeta strictly numbers order integral relation case positive psi

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SubjectPredicateObjectConfidenceSrc
Polygamma functionrelated to Integral representationWhen0.60section
Polygamma functionrelated to Integral representationRe0.60section
Polygamma functionrelated to Integral representationHurwitz0.60section
Polygamma functionrelated to Series representationThe0.60section
Polygamma functionrelated to Series representationThis0.60section
Polygamma functionrelated to Series representationHurwitz0.60section
Polygamma functionsee alsoFactorialGamma0.60section

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