The Whittaker functions arise as solutions to the Whittaker differential equation. The linearly independent solutions to this equation are M_(k, m)(z) | congruent | z^(m + 1/2) e^(-z/2) sum_(n = 0)^∞ (m - k + 1/2)_n/(n!(2m + 1)_n) z^n | = | z^(1/2 + m) e^(-z/2)[1 + (1/2 + m - k)/(1!(2m + 1)) z + ((1/2 + m - k)(3/2 + m - k))/(2!(2m + 1)(2m + 2)) z^2 + ...] and M_(k, - m)(z), where is a confluent hypergeometric function of the second kind and (z)_n is a Pochhammer symbol.

associated Laguerre polynomial | confluent hypergeometric function of the second kind | Cunningham function | Kummer's formulas | Schlömilch's function