Faxén integral

In mathematics, the Faxén integral is the following integral
The integral is named after the Swedish physicist Olov Hilding Faxén, who published it in 1921 in his PhD thesis.

''n''-dimensional Faxén integral

More generally one defines the -dimensional Faxén integral as
with
for and
The parameter is only for convenience in calculations.

Properties

Let denote the Gamma function, then
For one has the following relationship to the Scorer function

Asymptotics

For we have the following asymptotics