Confluent hypergeometric function: Difference between revisions

Revision as of 02:57, 29 March 2017

Revision as of 13:55, 12 April 2017

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:<math>z\frac{d^2w}{dz^2} +(b-z)\frac{dw}{dz} -\left(\sum_{m=0}^M a_m z^m\right)w = 0</math> <ref>{{cite journal|last1=Campos|first1=LMBC|title=On Some Solutions of the Extended Confluent Hypergeometric Differential Equation|journal=Journal of Computational and Applied Mathematics|date=2001|volume=Elsevier|doi=10.1016/s0377-0427(00)00706-8|pages=177–200}}</ref>

{NB that for Mm=0 (or when the summation involves just one term), it reduces to the conventional Confluent Hypergeometric Equation}

Thus Confluent Hypergeometric Functions can be used to solve "most" second-order ordinary differential equations whose variable coefficients are all linear functions of {{mvar|z}}; because they can be transformed to the Extended Confluent Hypergeometric Equation. Consider the equation: