Mahler polynomial

Template:Multiple issues In mathematics, the Mahler polynomials g_n(x) are polynomials introduced by Mahler in his work on the zeros of the incomplete gamma function.

Mahler polynomials are given by the generating function

$\sum g_n(x)t^n/n!=\exp (x(1+t-e^t))$

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

The first few examples are Template:OEIS

$g_0=1;$

$g_1=0;$

$g_2=-x;$

$g_3=-x;$

$g_4=-x+3x^2;$

$g_5=-x+10x^2;$

$g_6=-x+25x^2-15x^3;$

$g_7=-x+56x^2-105x^3;$

$g_8=-x+119x^2-490x^3+105x^4;$

References

• Template:Citation

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