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Mahler polynomial

From Wikipedia, the free encyclopedia

In mathematics, the Mahler polynomials gn(x) are polynomials introduced by Mahler (1930) in his work on the zeros of the incomplete gamma function.

Mahler polynomials are given by the generating function

Which is close to the generating function of the Touchard polynomials.

The first few examples are (sequence A008299 in the OEIS)

References

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  • Mahler, Kurt (1930), "Über die Nullstellen der unvollständigen Gammafunktionen.", Rendiconti Palermo (in German), 54: 1–41, doi:10.1007/BF03021175, JFM 56.0310.01