Jacobi identity

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21: Bibliography L

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Lie algebraic approaches to classical partition identities. Adv. in Math. 29 (1), pp. 15–59.

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ISSN 0001-8708, Document, MathReview (S. I. Gel’fand), ZentralBlatt

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§17.16.

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A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities. Adv. in Math. 45 (1), pp. 21–72.

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ISSN 0001-8708, Document, MathReview (George E. Andrews), ZentralBlatt

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§17.16.

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Co-recursive associated Jacobi polynomials. J. Comput. Appl. Math. 57 (1-2), pp. 203–213.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§18.30(i).

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Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray. Math. Comp. 17 (84), pp. 395–404.

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FullText, MathReview (I. A. Stegun), ZentralBlatt

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2nd item.

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22: 18.21 Hahn Class: Interrelations

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Hahn $\to$ Jacobi

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18.21.5 $$\underset{N\to \mathrm{\infty }}{lim}{Q}_n(Nx;\alpha ,\beta ,N)=\frac{P_n^{(\alpha ,\beta )}\left(1-2x\right)}{P_n^{(\alpha ,\beta )}\left(1\right)}.$$

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Symbols:

$Q_n(x;\alpha ,\beta ,N)$: Hahn polynomial, $P_n^{(\alpha ,\beta )}\left(x\right)$: Jacobi polynomial, $N$: positive integer, $n$: nonnegative integer and $x$: real variable

Referenced by:

§18.21(ii)

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http://dlmf.nist.gov/18.21.E5

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Annotations for §18.21(ii), §18.21(ii), §18.21 and Ch.18

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Figure 18.21.1: Askey scheme. … Magnify

23: Bibliography M

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An elementary proof of the Macdonald identities for $A_l^{(1)}$ . Adv. in Math. 57 (1), pp. 34–70.

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ISSN 0001-8708, Document, MathReview (Y. Lehrer-Ilamed), ZentralBlatt

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§17.15.

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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Ramanujan J. 6 (1), pp. 7–149.

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Document, ZentralBlatt

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§27.13(iv).

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New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function. Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.

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ISSN 0027-8424, MathReview (Ken Ono), ZentralBlatt

Referenced by:

§27.13(iv).

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24: 17.8 Special Cases of ${}_r{}^{}\psi _r^{}$ Functions

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Jacobi’s Triple Product

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Quintuple Product Identity

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25: 18.36 Miscellaneous Polynomials

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§18.36(i) Jacobi-Type Polynomials

►These are OP’s on the interval $(-1,1)$ with respect to an orthogonality measure obtained by adding constant multiples of “Dirac delta weights” at $-1$ and $1$ to the weight function for the Jacobi polynomials. … ►The possibility of generalization to $\alpha =-k$, for $k\in \mathbb{N}$, is implicit in the identity Szegő (1975, page 102), … ►

18.36.7 $$T_k(y)\equiv -x{y}^{\prime \prime }+\frac{x-k}{x+k}((x+k+1)y^{\prime }-y)=(n-1)y.$$

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Symbols:

$\equiv$: equals by definition, $y$: real variable, $k$: nonnegative integer, $n$: nonnegative integer and $x$: real variable

Referenced by:

§18.36(vi)

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http://dlmf.nist.gov/18.36.E7

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Addition (effective with 1.2.0):

This equation was added.

See also:

Annotations for §18.36(vi), §18.36(vi), §18.36 and Ch.18

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26: Bibliography W

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An algorithmic proof theory for hypergeometric (ordinary and “$q$”) multisum/integral identities. Invent. Math. 108, pp. 575–633.

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ISSN 0020-9910, Document, MathReview (David R. Masson), ZentralBlatt

Referenced by:

§16.4(iii).

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Rational function certification of multisum/integral/“$q$” identities. Bull. Amer. Math. Soc. (N.S.) 27 (1), pp. 148–153.

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ISSN 0273-0979, Pdf, Document, MathReview (Robert A. Gustafson), ZentralBlatt

Referenced by:

§16.4(iii).

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Explicit formulas for the associated Jacobi polynomials and some applications. Canad. J. Math. 39 (4), pp. 983–1000.

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ISSN 0008-414X, MathReview (W. A. Al-Salam), ZentralBlatt

Referenced by:

§18.30(i), §18.30.

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Asymptotic monotonicity of the relative extrema of Jacobi polynomials. Canad. J. Math. 46 (6), pp. 1318–1337.

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ISSN 0008-414X, MathReview (S. I. Drobnies), ZentralBlatt

Referenced by:

§18.14(iii).

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Estimates for the error term in a uniform asymptotic expansion of the Jacobi polynomials. Anal. Appl. (Singap.) 1 (2), pp. 213–241.

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ISSN 0219-5305, Document, MathReview (Eberhard Wagner), ZentralBlatt

Referenced by:

§18.15(i), §18.15(i).

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