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The Bessel functions  ,  ,  , and  are particular cases of more general functions: hypergeometric and Meijer G functions.
In particular, the functions  and  can be represented through the regularized hypergeometric functions  (without any restrictions on the parameter  ):
Similar formulas, but with restrictions on the parameter  , represent  and  through the classical hypergeometric function  :
The functions  and  can also be represented through the hypergeometric functions  by the following formulas:
Similar formulas for other Bessel functions  and  always include restrictions on the parameter, namely  :
In the case of integer  , the right‐hand sides of the preceding six formulas evaluate to removable indeterminate expressions of the type  ,  . The limit of the right‐hand sides exists and produces complicated series expansions including logarithmic and polygamma functions. These difficulties can be removed by using the generalized Meijer G function. The generalized Meijer G function allows represention of all four Bessel functions for all values of the parameter  by the following simple formulas:
The classical Meijer G function is less convenient because it can lead to additional restrictions:
Each of the Bessel functions can be represented through other Bessel functions:
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