In mathematics, the Faxén integral (also named Faxén function) 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 and 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
References