Paper:Harry Bateman/Some Properties of a certain Set of Polynomials

Harry Bateman: Some Properties of a certain Set of Polynomials

Published $1933$, Tohoku Mathematical Journal.

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Contents

1. The generating function.

2. Transformation of the generating function.

3. Expansion of a polynomial in a series of factorials.

4. Proof of the operational equation.

5. Recurrence relations.

6. Definite integrals for $F_n(z)$

7. The sign of $F_n(z)$ when $z$ is real.

8. Expansion of the exponential function.

9. Expansion of a factorial.

10. The power for $F_n(z)$.