A new twist on the Nuttall function Q_m,n(a,b)

Abstract

New expressions for the Nuttall function $Q_{m,n}(a,b)$ are given in terms of the confluent Appell function ${\mathrm{\Phi }}_3(c;d;x,y)$. The derived closed-form expressions are valid for integer values of m and n satisfying $m>n$ with $m+n$ being an odd integer; this happens to be the case of many practical applications involving the Nuttall Q-function.

Keywords:

• hypergeometric functions
• Nuttall Q-function
• Marcum Q-function
• special functions
• residue

AMS Subject Classification:

• 33E20
• 33C65
• 94A05

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The work of F. J. Lopez-Martinez was partially supported by Junta de Andalucia under project P11-TIC-7109, the Spanish Government and FEDER under projects TEC2013-44442 and COFUND2013-40259, the University of Malaga and the European Union under Marie-Curie COFUND U-mobility program (ref. 246550).

ORCID

F.J. Lopez-Martinez http://orcid.org/0000-0003-0233-6942

D. Morales-Jimenez http://orcid.org/0000-0002-2141-7185

Notes

1. or regularized bivariate confluent hypergeometric function