View source for Todd polynomials

{{TEX|done}}{{MSC|57R}}

A sequence of polynomials with rational number coefficients associated with [[Todd class]]es.

Let 
$$
H(z; \xi_1,\ldots,\xi_s) = \prod_{i=1}^s \frac{z \xi_i}{1 - \exp(-z\xi_i)} \ .
$$
The $m$-th Todd polynomial $T_m(c_1,\ldots,c_m)$ is defined by $T_m(\sigma_1,\ldots,\sigma_m)$ being the coefficient of $z^m$ in the power series expansion of $H(z; \xi_1,\ldots,\xi_m)$ where the $\sigma_i$ are the [[elementary symmetric function]]s of the $\xi_i$.

We have $T_1(c_1) = \frac12 c_1$, $T_2(c_1,c_2) = \frac1{12}(c_1^2 + c_2)$, $T_3(c_1,c_2,c_3) = \frac{1}{24}c_1c_2$.

The Todd polynomials are derived from the [[multiplicative sequence]] corresponding to the [[power series]] $t/(1-e^{-t})$.

==References==
* Hirzebruch, Friedrich. ''Topological methods in algebraic geometry'',  Classics in Mathematics. Translation from the German and appendix one by R. L. E. Schwarzenberger. Appendix two by A. Borel. Reprint of the 2nd, corr. print. of the 3rd ed. [1978] Berlin: Springer-Verlag (1995). {{ISBN|3-540-58663-6}}. {{ZBL|0843.14009}}.