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Legendre polynomials in irrationality proofs

Published online by Cambridge University Press:  17 April 2009

F. Beukers
F. Beukers
Affiliation:
Mathematisc Institut, Rijksuniversiteit Leiden, Wassenarseweg 80, Postbus 9512, 2300 RA Leiden, Netherlands.
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Abstract

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It is shown that a simple trick involving Legendre polynomials readily yields the irrationality of ea, , π2, and of the zeros of Bessel functions of integer order. Generalisation of this idea yields the irrationality of ζ(3).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 3 , December 1980 , pp. 431 - 438
Copyright
Copyright © Australian Mathematical Society 1980

References

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