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Mott Polynomial

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Polynomials s_k(x) which form the Sheffer sequence for

f(t)=-(2t)/(1-t^2)
(1)

and have exponential generating function

sum_(k=0)^infty(s_k(x))/(k!)t^k=exp[(x(1-sqrt(1+t^2)))/t].
(2)

The first few are

s_0(x)=1
(3)
s_1(x)=-1/2x
(4)
s_2(x)=1/4x^2
(5)
s_3(x)=1/8(-x^3+6x)
(6)
s_4(x)=1/(16)(x^4-24x^2)
(7)
s_5(x)=1/(32)(-x^5+60x^3-240x).
(8)

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References

Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 3. New York: Krieger, p. 251, 1981.Roman, S. The Umbral Calculus. New York: Academic Press, 1984.

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Mott Polynomial

Cite this as:

Weisstein, Eric W. "Mott Polynomial." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MottPolynomial.html

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