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In mathematics, the Faxén integral (also named Faxén function) is the following integral[1]
The integral is named after the Swedish physicist Olov Hilding Faxén, who published it in 1921 in his PhD thesis.[2]
n-dimensional Faxén integral[edit]
More generally one defines the -dimensional Faxén integral as[3]
with
- and
for and
The parameter is only for convenience in calculations.
Properties[edit]
Let denote the Gamma function, then
For one has the following relationship to the Scorer function
Asymptotics[edit]
For we have the following asymptotics[4]
References[edit]