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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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...
متن کاملMiniaturized Tables of Bessel Functions . II
In a previous study, we discussed the expansion of two-parameter functions in a double series of Chebyshev polynomials, and, in particular, we presented coefficients for the evaluation of the modified Bessel function (2z I iifne'K,(z) to 20 decimals for all z ^ 5 and all v, 0 g v g 1. In the present study, we give similar coefficients for the evaluation of ge~'z-»l,(z) to at least 20 decimals w...
متن کاملThe Circle Problem and Double Series of Bessel Functions
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...
متن کاملLogarithmic Means and Double Series of Bessel Functions
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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1950
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1950-0037924-6