Exponential integral

In mathematics, the Integralexponentialfunktion than

Defined.

Since diverges, the above integral for the Cauchy principal value is to be understood.

The Integralexponentialfunktion has the series representation

Where ln is the natural logarithm and the Euler - Mascheroni constant.

The Integralexponentialfunktion is closely related to the logarithmic integral, it is

Also closely related is a function that integrates over a different range of integration:

This function may be regarded as an extension of Integralexponentialfunktion negative real values ​​, since

Both functions can be jointly expressed as a whole function:

Through this function the other two as

And

Represent.

The Integralexponentialfunktion is a special case of the incomplete gamma function

They can also act as

Be generalized.

Swell

• William H. Press et al.: Numerical Recipes ( FORTRAN ). Cambridge University Press, New York 1989.
• Milton Abramowitz and Irene A. Stegun (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York 1972. (See Chapter 5)
• R. D. Misra: Proc. Cambridge Phil Soc. Volume 36, 1940, p 173 ( Please check After JFM doubtful disconcerting title: . On the stability of crystal lattices II, p.173 -182 )