Tricomi confluent hypergeometric function: Differential equations (formula 07.33.13.0011)

HypergeometricU

$Mathematica Notation$

Hypergeometric Functions

HypergeometricU[a,b,z]

Differential equations

Ordinary linear differential equations and wronskians

For the direct function itself

http://functions.wolfram.com/07.33.13.0011.01

Input Form

z^2 Derivative[2][w][z] + (1 - 2 s + r (-1 + b - d z^r)) z Derivative[1][w][z] + (s (r - b r + s) + d r ((-a) r + s) z^r) w[z] == 0 /; w[z] == Subscript[c, 1] z^s Hypergeometric1F1Regularized[a, b, d z^r] + Subscript[c, 2] z^s HypergeometricU[a, b, d z^r]

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02