Hyperbolic tangent: Differentiation (formula 01.21.20.0007)

Tanh

$Mathematica Notation$

Elementary Functions

Tanh[z]

Differentiation

Fractional integro-differentiation

http://functions.wolfram.com/01.21.20.0007.01

Input Form

Derivative[\[Alpha]][Tanh][c z] == (-I)^(1 - \[Alpha]) ((Log[4] (I c z)^(-1 - \[Alpha]))/Gamma[-\[Alpha]]) - ((-I)^(1 - \[Alpha]) Pi^(-1 - \[Alpha]) (((-I) c z)^\[Alpha] (2^(1 + \[Alpha]) PolyGamma[\[Alpha], -((2 I c z)/Pi)] - PolyGamma[\[Alpha], -((I c z)/Pi)]) + (I c z)^\[Alpha] (PolyGamma[\[Alpha], (I c z)/Pi] - 2^(1 + \[Alpha]) PolyGamma[\[Alpha], (2 I c z)/Pi])))/(I c z)^\[Alpha]

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02