Confluent hypergeometric series

Furthermore, from the properties of the confluent hypergeometric series,... 

Equation (137b) is obtained from (137a) by the use of (112). Equation (137c) is derived by using the definition of the confluent hypergeometric series (114). One sees that the following equation holds when t - oo ... 

One of the most utilized methods for solving the radial equation is by expanding the wave function as a power series of the radial coordinate. This approach is very appropriate because the power series [1-3,30-32,34, 35] correctly represents the confluent hypergeometric function. 

The confluent hypergeometric function F(A, C, z) of the complex variable 2 is defined by the series... 

Similar conclusions have been obtained by Wallach [12]. More detailed approximate results may be obtained by using only one delay group equation rather than six. In this case, elimination of C between the equations for N and C results in a second order differential equation for N which for constant dpjdt is a confluent hypergeometric equation. Results similar to those obtained by the above methods have been obtained by Elrod [13] using series expansions in inverse powers of a. 

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