Article · Wikipedia archive · Last revised Jul 25, 2026

Pincherle polynomials

In mathematics, the Pincherle polynomials Pn(x) are polynomials introduced by S. Pincherle (1891) given by the generating function

Last revised
Jul 25, 2026
Read time
≈ 1 min
Length
100 w
Citations
1
Source

In mathematics, the Pincherle polynomials Pn(x) are polynomials introduced by S. Pincherle (1891)1 given by the generating function

( 1 3 x t + t 3 ) 1 / 2 = n = 0 P n ( x ) t n {\displaystyle \displaystyle (1-3xt+t^{3})^{-1/2}=\sum _{n=0}^{\infty }P_{n}(x)t^{n}}

Humbert polynomials are a generalization of Pincherle polynomials

References

References

  1. Pincherle, Salvatore (1891), "Una nuova estensione delle funzioni sferiche", Memorie della Accademia Reale di Bologna (in Italian), I: 337–369, JFM 23.0514.01
Further reading

Further reading

  • Humbert, Pierre (1921), "Some extensions of Pincherle's Polynomials", Proceedings of the Edinburgh Mathematical Society, 39: 21–24, doi:10.1017/S0013091500035756