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Sharpe's Differential Equation

A generalization of the Bessel Differential Equation for functions of order 0, given by


Solutions are

y=e^{\pm iz} {}_1F_1\left({{\textstyle{1\over 2}}\mp {\textstyle{1\over 2}}iA; 1; \mp 2iz}\right),

where ${}_1F_1(a;b;x)$ is a Confluent Hypergeometric Function.

See also Bessel Differential Equation, Confluent Hypergeometric Function

© 1996-9 Eric W. Weisstein