A Family of Entire Functions Connecting the Bessel Function J1 and the Lambert W Function

Motivated by the problem of determining the values of α > 0 for which f α ( x ) = e α - ( 1 + 1 / x ) α x , x > 0 , is a completely monotonic function, we combine Fourier analysis with complex analysis to find a family φ α , α > 0 , of entire functions such that f α ( x ) = ∫ 0 ∞ e - s x φ...

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Veröffentlicht in:	Constructive approximation 2021, Vol.53 (1), p.121-154
Hauptverfasser:	Berg, Christian, Massa, Eugenio, Peron, Ana P.
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Bessel functions Combinatorial analysis Entire functions Fourier analysis Mathematics Mathematics and Statistics Numerical Analysis Polynomials Power series Series expansion Thermal expansion
Online-Zugang:	Volltext
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