Connections within the group of differentiated gamma functions and with other function groups
Representations through more general functions
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:
Representations through related equivalent functions
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:
Representations through other differentiated gamma functions
The differentiated gamma functions , , , and are interconnected through the following formulas:
