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Cunningham Function

Sometimes also called the Pearson-Cunningham Function. It can be expressed using Whittaker Functions (Whittaker and Watson 1990, p. 353).

\omega_{n,m}(x)\equiv {e^{\pi i(m/2-n)+x}\over \Gamma(1+n-{\textstyle{1\over 2}}m)} U({\textstyle{1\over 2}}m-n, 1+m, x),

where $U(a,b,z)$ is a Confluent Hypergeometric Function of the Second Kind (Abramowitz and Stegun 1972, p. 510).

See also Confluent Hypergeometric Function of the Second Kind, Whittaker Function


Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.

Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.

© 1996-9 Eric W. Weisstein