منابع مشابه
Integral Representation for Neumann Series of Bessel Functions
A closed integral expression is derived for Neumann series of Bessel functions — a series of Bessel functions of increasing order — over the set of real numbers.
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Ramanujan’s lost notebook, along with various fragments and partial manuscripts, was published in 1988. One fragment (page 335) contains two formulas involving finite trigonometric sums and doubly infinite series of Bessel functions, which are connected with the classical circle and divisor problems. For the first time, we provide a proof of the first identity in the formulation given by Ramanu...
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Manuscript Number: Full Title: Logarithmic Means and Double Series of Bessel Functions Article Type: Research Paper Section/Category: SPECIAL ISSUE in Memory of Paul Bateman and Heini Halberstam
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Recently Pogány and Süli [Proc. Amer. Math. Soc. 137(7) (2009), 2363–2368] derived a closed-form integral expression for Neumann series of Bessel functions of the first kind Jν . In this paper our aim is to establish analogous integral representations for the Neumann-type series of modified Bessel functions of the first kind Iν and for Bessel functions of the second kind Yν , Kν , and to give l...
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A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1938
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500008439