Definition of Sonine. Meaning of Sonine. Synonyms of Sonine

Here you will find one or more explanations in English for the word Sonine. Also in the bottom left of the page several parts of wikipedia pages related to the word Sonine and, of course, Sonine synonyms and on the right images related to the word Sonine.

Definition of Sonine

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Meaning of Sonine from wikipedia

- In mathematics, Sonine's formula is any of several formulas involving Bessel functions found by Nikolay Yakovlevich Sonin. One such formula is the following...
- be done here (alternatively ****ociated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor Nikolay Yakovlevich Sonin). More generally...
- 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...
- the Bessel functions is the Poisson representation formula and the Mehler-Sonine formula: J ν ( z ) = ( z 2 ) ν Γ ( ν + 1 2 ) π ∫ − 1 1 e i z s ( 1 − s 2...
- orthogonal polynomials from the others. The first condition was found by Sonine (and later by Hahn), who showed that (up to linear changes of variable)...
- t-{\dfrac {v\pi }{2}}\right)\cosh vt~dt\end{aligned}}} With the Mehler–Sonine integral expressions of J v ( z ) = 2 π ∫ 0 ∞ sin ⁡ ( z cosh ⁡ t − v π 2...
- \sum _{k=0}(-1)^{k}J_{s+2k}(z)(s+2k){-s \choose k},} or the more general Sonine formula e i γ z = Γ ( s ) ⋅ ∑ k = 0 i k C k ( s ) ( γ ) ( s + k ) J s +...