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variants of this functions
PolyGamma






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Gamma, Beta, Erf > PolyGamma[z] > Introduction to the differentiated gamma functions





Connections within the group of differentiated gamma functions and with other function groups


The differentiated gamma functions , , , and are particular cases of the more general hypergeometric and Meijer G functions. Although the arguments of these functions do not depend on the variable , it is included in their parameters.

For example, , , , and can be represented through generalized hypergeometric functions by the following formulas:

The aforementioned general formulas can be rewritten using the classical Meijer G functions as follows:

The differentiated gamma functions , , , and can be represented through derivatives of the gamma function :

The differentiated gamma functions , , , and can also be represented through derivatives of the logarithm of the gamma function :

The functions and are intimately related to the Hurwitz zeta function and the Bernoulli polynomials and numbers , by the formulas:

The differentiated gamma functions , , , and are interconnected through the following formulas:





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