Hermite identity

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)