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Methods of Mathematical Physics, Third Edition by Bertha Jeffreys, Harold Jeffreys

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Chapter 23THE CONFLUENT HYPERGEOMETRIC FUNCTION

‘All changes trying, he will take the formOf ev’ry reptile on the earth, will seemA river now, and now devouring fire;But hold him ye, and grasp him still the more.’

HOMER, Odyssey (Cowper’s translation)

23·01.

The hypergeometric function is defined in general by the series

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and satisfies the differential equation

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A second solution is

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It can be shown by direct transformation that any second order ...

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