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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:Physics
gptkb:quantum_field_theory
gptkb:Number_theory
gptkb:Probability_theory
Statistics
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gptkbp:asymptoticExpansion
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ψ⁽ⁿ⁾(z) ~ (-1)^{n+1} n! ∑_{k=0}^∞ B_{k+n+1}/(k+n+1) z^{k+n+1}
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gptkbp:citation
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gptkb:NIST_Digital_Library_of_Mathematical_Functions
gptkb:Handbook_of_Mathematical_Functions_(Abramowitz_and_Stegun)
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gptkbp:defines
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nth derivative of the digamma function
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gptkbp:differential
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ψ⁽ⁿ⁾(z) = dⁿ⁺¹/dzⁿ⁺¹ ln Γ(z)
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gptkbp:domain
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gptkb:Complex_numbers
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gptkbp:field
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gptkb:Mathematics
gptkb:Mathematical_analysis
Special functions
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gptkbp:firstPolygamma
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gptkb:Digamma_function
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gptkbp:hasSpecialCase
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ψ⁽⁰⁾(z) = Digamma function
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https://www.w3.org/2000/01/rdf-schema#label
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Polygamma function
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gptkbp:notation
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ψ⁽ⁿ⁾(z)
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gptkbp:order
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n (non-negative integer)
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gptkbp:recurrence
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ψ⁽ⁿ⁾(z+1) = ψ⁽ⁿ⁾(z) + (-1)ⁿ n! / zⁿ⁺¹
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gptkbp:relatedTo
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gptkb:Hurwitz_zeta_function
gptkb:Bernoulli_numbers
gptkb:Gamma_function
gptkb:Digamma_function
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gptkbp:seriesRepresentation
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ψ⁽ⁿ⁾(z) = (-1)^{n+1} n! ∑_{k=0}^∞ 1/(z+k)^{n+1}
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gptkbp:bfsParent
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gptkb:Gamma_function
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gptkbp:bfsLayer
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6
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