Hadamard product of series with special numbers. (English) Zbl 1527.40002
Summary: We evaluate in closed form a large class of power series where the coefficients are products of special numbers, or products of special numbers and Laguerre polynomials. A number of examples is presented involving harmonic, hyperharmonic, Fibonacci, Lucas, Bernoulli, Euler, and derangement numbers. We also obtain a new convolution formula for the Laguerre polynomials.
MSC:
| 40A05 | Convergence and divergence of series and sequences |
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
summation of series; Hadamard product of series; binomial series; Bernoulli numbers; Euler numbers; Fibonacci numbers; harmonic numbers; hyperharmonic numbers; derangement numbers; Laguerre polynomialsReferences:
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