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
 |
where 
is a polynomial in 
and
 |
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