Polynomials 
which form the Sheffer sequence for
 |  |  |
(1)
|
 |  |  |
(2)
|
which have generating function
![sum_(k=0)^infty(s_k(x))/(k!)t^k=[t/(ln(1+t))]^a(1+t)^x.](/images/equations/NarumiPolynomial/NumberedEquation1.svg) |
(3)
|
The first few are
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  | ![1/(12)[12x^2+12(a-1)x+a(3a-5)].](/images/equations/NarumiPolynomial/Inline16.svg) |
(6)
|
Narumi Polynomial
Explore with Wolfram|Alpha
References
Boas, R. P. and Buck, R. C. Polynomial Expansions of Analytic Functions, 2nd print., corr. New York: Academic Press, p. 37, 1964.Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 3. New York: Krieger, p. 258, 1981.Roman, S. The Umbral Calculus. New York: Academic Press, 1984.Referenced on Wolfram|Alpha
Narumi PolynomialCite this as:
Weisstein, Eric W. "Narumi Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NarumiPolynomial.html