- Clausen's formula
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In mathematics, Clausen's formula, found by Thomas Clausen (1828), expresses the square of a Gaussian hypergeometric series as a generalized hypergeometric series. It states
In particular it gives conditions for a hypergeometric series to be positive. This can be used to prove several inequalities, such as the Askey–Gasper inequality used in the proof of de Branges's theorem.
References
- Andrews, George E.; Askey, Richard; Roy, Ranjan (1999), Special functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge University Press, ISBN 978-0-521-62321-6; 978-0-521-78988-2, MR1688958
- Clausen, Thomas (1828), "Ueber die Fälle, wenn die Reihe von der Form y = 1 + ... etc. ein Quadrat von der Form z = 1 ... etc.hat", Journal für die reine und angewandte Mathematik 3, http://www.digizeitschriften.de/main/dms/toc/?PPN=PPN243919689_0003
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