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The exponential integrals  ,  ,  ,  ,  ,  , and  are the particular cases of the more general hypergeometric and Meijer G functions.
For example, they can be represented through hypergeometric functions  or the Tricomi confluent hypergeometric function  :
Representations of the exponential integrals  and  , the sine and cosine integrals  and  , and the hyperbolic sine and cosine integrals  and  through classical Meijer G functions are rather simple:
Here  is the Euler gamma constant and the complicated‐looking expression containing the two logarithm simplifies piecewise:
But the last four formulas that contain the Meijer G function can be simplified further by changing the classical Meijer  functions to the generalized one. These formulas do not include factors  and terms  :
The corresponding representations of the logarithmic integral  through the classical Meijer G function is more complicated and includes composition of the G function and a logarithmic function:
All six exponential integrals of one variable are the particular cases of the incomplete gamma function:
The exponential integral  can be represented through the incomplete gamma function or the regularized incomplete gamma function:
The exponential integral  is connected with the inverse of the regularized incomplete gamma function  by the following formula:
The exponential integrals  ,  ,  ,  ,  ,  , and  are interconnected through the following formulas:
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