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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

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

References

• Wright, E. M. (1934), "The asymptotic expansion of the generalized Bessel function.", Proceedings of the London Mathematical Society: 257–270, doi: 10.1112/plms/s2-38.1.257, JFM  60.0306.02

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