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Sharpe's Differential Equation

Sharpe's differential equation generalizes the Bessel differential equation for functions of order 0 and is 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

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Cite this as:

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

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