Hermite identity
From Encyclopedia of Mathematics
An identity applied by Ch. Hermite (1873) to certain specially constructed polynomials in the proof that the number is transcendent. In a simplified form it is
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where is a polynomial in
and
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Comments
For a proof of the transcendence of and use of Hermite's identity see, e.g., [a1], Thm. 6.4. There a simplified version of Hermite's original proof is given.
References
[a1] | I. Stewart, "Galois theory" , Chapman & Hall (1979) |
How to Cite This Entry:
Hermite identity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hermite_identity&oldid=33581
Hermite identity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hermite_identity&oldid=33581