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

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Chapter 15THE FACTORIAL AND RELATED FUNCTIONS

‘There are three hundred and seventy-two competent renderings of a single verse of one of the more cryptic Odes, and it has been aptly claimed that even the appearance of a giraffe must be capable of some rational explanation.’

EBNEST BHAMAH, The Moon of much Gladness.

15·01. We define the factorial function*

by

images

    where images(z) ≥ – 1. Convergence is uniform in any region images(z) ≥ – 1 + δ, where δ > 0.

     ...

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