Bessel–Maitland function

In mathematics, the Bessel–Maitland function, or Wright generalized Bessel function, is a generalization of the Bessel function, introduced by Edward Maitland Wright (1934). The word "Maitland" in the name of the function seems to be the result of confusing Edward Maitland Wright's middle and last names. It is given by

J^{\mu ,\nu }(z)=\sum _{k\geq 0}{\frac {(-z)^{k}}{\Gamma (k\mu +\nu +1)k!}}.

References

Wright, E. M. (1934), The asymptotic expansion of the generalized Bessel function., doi:10.1112/plms/s2-38.1.257, JFM 60.0306.02

This article is issued from Wikipedia - version of the 8/22/2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.