Formulas derived from moment generating functions and Bernstein polynomials. (English) Zbl 1499.11154
Summary: The purpose of this paper is to provide some identities derived by moment generating functions and characteristics functions. By using functional equations of the generating functions for the combinatorial numbers \(y_1(m,n;\lambda)\), defined in [Y. Simsek, Appl. Anal. Discrete Math. 12, No. 1, 1–35 (2018; Zbl 1488.11072)] p. 8, Theorem 1], we obtain some new formulas for moments of discrete random variable that follows binomial (Newton) distribution with an application of the Bernstein polynomials. Finally, we present partial derivative formulas for moment generating functions which involve derivative formula of the Bernstein polynomials.
MSC:
| 11B83 | Special sequences and polynomials |
| 05A15 | Exact enumeration problems, generating functions |
| 05A19 | Combinatorial identities, bijective combinatorics |
Keywords:
distribution functions; special polynomials and numbers; characteristic function; generating functions; combinatorial identitiesCitations:
Zbl 1488.11072References:
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