A series transformation formula and related polynomials

Khristo N. Boyadzhiev

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-18

Abstract:

We present a formula that turns power series into series of functions. This formula serves two purposes: first, it helps to evaluate some power series in a closed form; second, it transforms certain power series into asymptotic series. For example, we find the asymptotic expansions for λ > 0 of the incomplete gamma function γ ( λ , x ) and of the Lerch transcendent Φ ( x , s , λ ) . In one particular case, our formula reduces to a series transformation formula which appears in the works of Ramanujan and is related to the exponential (or Bell) polynomials. Another particular case, based on the geometric series, gives rise to a new class of polynomials called geometric polynomials.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:792107

DOI: 10.1155/IJMMS.2005.3849

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