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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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9.2 Confluent Hypergeometric Functions

9.20 Introduction

9.20110 A confluent hypergeometric function is obtained by taking the limit as c→∞ in the solution of Riemann's differential equation

u=P{ 0c12+μccλz12μ0λ }

si188_e  WH

9.202 The equation obtained by means of this limiting process is of the form

1. 

d2udz2+dudz+(λz+14μ2z2)u=0

si189_e  WH

Equation 9.202 1 has the following two linearly independent solutions:

2. 

z12+μezΦ(12+μλ,2μ+1;z)

si190_e

3. 

z

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