Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











CoshIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CoshIntegral[z] > Introduction to the exponential integrals





Connections within the group of exponential integrals and with other function groups

Representations through more general functions

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:

Representations through related equivalent functions

The exponential integral can be represented through the incomplete gamma function or the regularized incomplete gamma function:

Relations to inverse functions

The exponential integral is connected with the inverse of the regularized incomplete gamma function by the following formula:

Representations through other exponential integrals

The exponential integrals , , , , , , and are interconnected through the following formulas: