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Computer-assisted construction of Ramanujan-Sato series for 1 over π. [PDF]

Ramanujan J
Hemmecke R, Paule P, Radu CS.
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Relativistic jacobi polynomials

Integral Transforms and Special Functions, 1999
A new polynomials set, of generalized hypergeometric type, is defined. These polynomials, called relativistic Jacobi polynomials (RJP) and denoted by represent an extension of the classical Jacobi orthogonal polynomials in the sense that they reduce to the latter in the non-relativistic limit (N → ∞). Some basic properties of these polynomials, as well
He, Matthew, Natalini, P.
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The Zeros of Certain Jacobi Polynomials

SIAM Journal on Mathematical Analysis, 1982
Two theorems are proved about the zeros of certain Jacobi polynomials that are important in the theory of interpolation and approximation.THEOREM 1. Let$S_k $and$\bar S_k $be the sums of thekth powers of the zeros of$P_n^{(w, - w)} (x)$and$P_n^{(w, - w)} ( - x)$respectively (wreal, $0 < w < 1$). Then for$k = 1,2, \cdots ,2n,S_k - \bar S_k = - 2w$ (kodd)
Young, Andrew, Hamideh, Hassan
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A REMARK ON JACOBI POLYNOMIAL ESTIMATES

International Journal of Wavelets, Multiresolution and Information Processing, 2009
In this paper, an estimate of Jacobi polynomials with complex indices is proved. It improves a corresponding result of Ref. 2.
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On Jacobi polynomials

Mathematical Proceedings of the Cambridge Philosophical Society, 1969
1. The object of this paper is to prove some formulae of Jacobi polynomials including a generating function. The results (2·l)–(2·4), (2·6)–(2·9), (3·l)–(3·4), and (4·1) are believed to be new.
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Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients

Mathematical Proceedings of the Cambridge Philosophical Society, 1971
The answers to many important questions in the harmonic analysis of orthogonal polynomials are known to depend on the determination of when formulas of the typesand their dualshold, where pn(x) and qn(x) are suitably normalized orthogonal polynomials or orthogonal polynomials multiplied by certain functions; e.g. e−pxLn(x).
Askey, R., Gasper, G.
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A Generating Function for Jacobi Polynomials

Canadian Mathematical Bulletin, 1966
The following notations will be employed throughout this note.The object of the present note is to obtain a new generating function for the Jacobi polynomials defined by [4, page 268]
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Asymptotics of generalized jacobi polynomials

Constructive Approximation, 1986
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On the zeros of subrange Jacobi polynomials

Numerical Algorithms, 2017
All positive zeros of subrange Jacobi polynomials, orthogonal on [−c, c], 0 < c − 1, β > − 1, are shown in the ultraspherical case α = β, and partly conjectured in the general case α < β, to be monotonically increasing as functions of c.
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Sub-range Jacobi polynomials

Numerical Algorithms, 2012
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