TOPICS
Search

Sharpe's Differential Equation

A generalization of the Bessel differential equation for functions of order 0, given by

zy^('')+y^'+(z+A)y=0.

Solutions are

y=e^(+/-iz)_1F_1(1/2∓1/2iA;1;∓2iz),

where _1F_1(a;b;x) is a confluent hypergeometric function of the first kind.

See also

Bessel Differential Equation, Confluent Hypergeometric Function of the First Kind

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Sharpe's Differential Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SharpesDifferentialEquation.html

Subject classifications