Definition of Sonine. Meaning of Sonine. Synonyms of Sonine

- In mathematics, Sonine's formula is any of several formulas involving Bessel functions found by Nikolay Yakovlevich Sonin. One such formula is the following...
- 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...
- be done here (alternatively ****ociated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor Nikolay Yakovlevich Sonin). More generally...
- 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 +...