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Sonine Formula
In mathematics, Sonine's formula is any of several formulas involving Bessel functions found by Nikolay Yakovlevich Sonin Nikolay Yakovlevich Sonin (Russian: Никола́й Я́ковлевич Со́нин, February 22, 1849 – February 27, 1915) was a Russian mathematician. Biography He was born in Tula and attended Lomonosov University, studying mathematic .... One such formula is the following integral formula involving a product of three Bessel functions: :\int_0^\infty J_z(at) J_z(bt)J_z(ct) t^\,dt = \frac where Δ is the area of a triangle with given sides. References *{{Citation , last1=Stempak , first1=Krzysztof , title=A new proof of Sonine's formula , doi=10.2307/2046994 , mr=962812 , year=1988 , journal= Proceedings of the American Mathematical Society , issn=0002-9939 , volume=104 , issue=2 , pages=453–457, jstor=2046994 Special hypergeometric functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex number \alpha, the ''order'' of the Bessel function. Although \alpha and -\alpha produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of \alpha. The most important cases are when \alpha is an integer or half-integer. Bessel functions for integer \alpha are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer \alpha are obtained when the Helmholtz equation is solved in spherical coordinates. Applications of Bessel functions The Bessel function is a generali ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikolay Yakovlevich Sonin
Nikolay Yakovlevich Sonin (Russian: Никола́й Я́ковлевич Со́нин, February 22, 1849 – February 27, 1915) was a Russian mathematician. Biography He was born in Tula and attended Lomonosov University, studying mathematics and physics there from 1865 to 1869. His advisor was Nikolai Bugaev. He obtained a master's degree with a thesis submitted in 1871, then he taught at the University of Warsaw where he obtained a doctorate in 1874. He was appointed to a chair in the University of Warsaw in 1876. In 1894, Sonin moved to St. Petersburg, where he taught at the University for Women. Sonin worked on special functions, in particular cylindrical functions. For instance, the Sonine formula is a formula given by Sonin for the integral of the product of three Bessel functions. He is furthermore credited with the introduction of the associated Laguerre polynomials.Sonine, N. Y. (1880): "Recherches sur les fonctions cylindriques et le développement des foncti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The American Mathematical Society
''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages. According to the ''Journal Citation Reports'', the journal has a 2018 impact factor of 0.813. Scope ''Proceedings of the American Mathematical Society'' publishes articles from all areas of pure and applied mathematics, including topology, geometry, analysis, algebra, number theory, combinatorics, logic, probability and statistics. Abstracting and indexing This journal is indexed in the following databases: 2011. American Mathematical Society. * |
