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

[math]\displaystyle{ J^{\mu,\nu}(z) = \sum_{k\ge 0} \frac{(-z)^k}{\Gamma(k\mu+\nu+1)k!}. }[/math]

References

• Wright, E. M. (1934), "The asymptotic expansion of the generalized Bessel function.", Proceedings of the London Mathematical Society: 257–270, doi:10.1112/plms/s2-38.1.257