Racah polynomials

Racah polynomials

In mathematics, Racah polynomials are orthogonal polynomials named after Giulio Racah, as their orthogonality relations are equivalent to his orthogonality relations for Racah coefficients.

The Racah polynomials were first defined by harvtxt|Wilson|1978 and are given by:p_n(x(x+gamma+delta+1)) = {}_4F_3left [egin{matrix} -n &n+alpha+eta+1&-x&x+gamma+delta+1\alpha+1&gamma+1&eta+delta+1\ end{matrix};1 ight]

harvtxt|Askey|Wilson|1979 introduced the "q"-Racah polynomials defined in terms of basic hypergeometric functions by:p_n(q^{-x}+q^{x+1}cd;a,b,c,d;q) = {}_4phi_3left [egin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\aq&bdq&cq\ end{matrix};q;q ight] They are sometimes given with changes of variables as:W_n(x;a,b,c,N;q) = {}_4phi_3left [egin{matrix} q^{-n} &abq^{n+1}&q^{-x}&cq^{x-n}\aq&bcq&q^{-N}\ end{matrix};q;q ight]

References

*Citation | last1=Askey | first1=Richard | last2=Wilson | first2=James | title=A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols | doi=10.1137/0510092 | id=MathSciNet | id = 541097 | year=1979 | journal=SIAM Journal on Mathematical Analysis | issn=0036-1410 | volume=10 | issue=5 | pages=1008–1016
*citation|first=J.|last= Wilson|title= Hypergeometric series recurrence relations and some new orthogonal functions|series= Ph.D. thesis|publisher= Univ. Wisconsin, Madison|year= 1978


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Discrete orthogonal polynomials — In mathematics, a sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with repect to a discrete measure. Examples include the discrete Chebyshev polynomials, Charlier polynomials, Krawtchouk… …   Wikipedia

  • Giulio Racah — Giulio (Yoel) Racah ( he. פרופסור (יואל) רקח; 1909 August 28, 1965) was an Italian Israeli physicist and mathematician.Born in Florence, Italy, he took his PhD from the University there in 1930, and later studied in Rome with Enrico Fermi. In… …   Wikipedia

  • Giulio Racah — Giulio (Yoel) Racah (פרופסור יואל רקח en hébreu) (1909 28 août 1965) est un physicien et mathématicien italiano israélien. Biographie Cette section est vide, insuffisamment détaillée ou incomplète …   Wikipédia en Français

  • Orthogonal polynomials — In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the… …   Wikipedia

  • Dual Hahn polynomials — In mathematics, the dual Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined in terms of generalized hypergeometric functions by for 0≤n≤N where λ(x)=x(x+γ+δ+1).… …   Wikipedia

  • List of polynomial topics — This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics.Basics*Polynomial *Coefficient *Monomial *Polynomial long division *Polynomial factorization *Rational function *Partial… …   Wikipedia

  • List of mathematics articles (R) — NOTOC R R. A. Fisher Lectureship Rabdology Rabin automaton Rabin signature algorithm Rabinovich Fabrikant equations Rabinowitsch trick Racah polynomials Racah W coefficient Racetrack (game) Racks and quandles Radar chart Rademacher complexity… …   Wikipedia

  • List of special functions and eponyms — This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differential operators of the theory (but not intended to include every mathematical eponym).… …   Wikipedia

  • Solid harmonics — In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates. There are two kinds: the regular solid harmonics R^m ell(mathbf{r}), which vanish at the origin and the irregular solid… …   Wikipedia

  • Multipole moment — In mathematics, especially as applied to physics, multipole moments are the coefficients of a series expansion of a potential due to continuous or discrete sources (e.g., an electric charge distribution). A multipole moment usually involves… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”