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On the Roots of Confluent Hypergeometric Functions

Published online by Cambridge University Press:  20 January 2009

Archd Milne
Affiliation:
Research Student, Edinburgh University Mathematical Laboratory.
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In the present paper the disposition of the roots of the confluent hypergeometric functions — denoted by Wk, m(z) — as affected by changing the parameters k and m is investigated. The results are then shewn in a graphical form, and various typical illustrations of the functions are given. By giving special values to k and m it is then exemplified how the roots of other functions expressible in terms of Wk, m(z) may be studied. The zeros of the parabolic cylinder functions are then discussed. Some of the properties of an allied class of functions, denoted by ψn(z), are then given, and finally, it is shewn how the properties of Abel's function φm(z) may be obtained from results already given.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1914

References

* The connexion of the φ-function with the W km-function was first noticed by H. Bateman.