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21: 34.3 Basic Properties: 3 ⁒ j Symbol
§34.3 Basic Properties: 3 ⁒ j Symbol
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§34.3(iv) Orthogonality
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22: Bibliography E
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  • M. Edwards, D. A. Griggs, P. L. Holman, C. W. Clark, S. L. Rolston, and W. D. Phillips (1999) Properties of a Raman atom-laser output coupler. J. Phys. B 32 (12), pp. 2935–2950.
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    External Links:
    FullText
    Referenced by:
    §12.17.
    Encodings:
    BibTeX
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  • Á. Elbert (2001) Some recent results on the zeros of Bessel functions and orthogonal polynomials. J. Comput. Appl. Math. 133 (1-2), pp. 65–83.
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    External Links:
    ISSN 0377-0427, Document, MathReview (N. Hayek Calil), ZentralBlatt
    Referenced by:
    §10.21(iv).
    Encodings:
    BibTeX
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  • Á. Elbert and A. Laforgia (1994) Interlacing properties of the zeros of Bessel functions. Atti Sem. Mat. Fis. Univ. Modena XLII (2), pp. 525–529.
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    External Links:
    ISSN 0041-8986, MathReview (Evangelos Ifantis), ZentralBlatt
    Referenced by:
    §10.21(i).
    Encodings:
    BibTeX
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  • A. Erdélyi (1941a) Generating functions of certain continuous orthogonal systems. Proc. Roy. Soc. Edinburgh. Sect. A. 61, pp. 61–70.
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    External Links:
    MathReview (G. SzegΕ‘), ZentralBlatt
    Referenced by:
    §12.16.
    Encodings:
    BibTeX
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  • W. N. Everitt (2008) Note on the X 1 -Laguerre orthogonal polynomials.
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    Notes:
    arXiv:0811.3559v2
    Referenced by:
    §18.36(vi).
    Encodings:
    BibTeX
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    23: Bibliography R
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  • S. Ramanujan (1921) Congruence properties of partitions. Math. Z. 9 (1-2), pp. 147–153.
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    External Links:
    ISSN 0025-5874, ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt
    Referenced by:
    §27.14(v).
    Encodings:
    BibTeX
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  • S. Ramanujan (1927) Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.). In Collected Papers,
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    Referenced by:
    §24.7(i).
    Encodings:
    BibTeX
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  • J. Raynal (1979) On the definition and properties of generalized 6 - j  symbols. J. Math. Phys. 20 (12), pp. 2398–2415.
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    External Links:
    ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt
    Referenced by:
    §16.4(iii), §16.4(iii).
    Encodings:
    BibTeX
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  • W. P. Reinhardt (2018) Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.
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    Notes:
    arXiv:1812.02196
    Referenced by:
    §18.40(ii).
    Encodings:
    BibTeX
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  • M. Robnik (1980) An extremum property of the n -dimensional sphere. J. Phys. A 13 (10), pp. L349–L351.
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    External Links:
    ISSN 0305-4470, Document, MathReview
    Referenced by:
    §5.19(iii).
    Encodings:
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    24: Bibliography S
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  • I. M. Sheffer (1939) Some properties of polynomial sets of type zero. Duke Math. J. 5, pp. 590–622.
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    External Links:
    ISSN 0012-7094, Link, MathReview (A. Erdélyi), ZentralBlatt
    Referenced by:
    §18.2(xii).
    Encodings:
    BibTeX
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  • I. Sh. SlavutskiΔ­ (1995) Staudt and arithmetical properties of Bernoulli numbers. Historia Sci. (2) 5 (1), pp. 69–74.
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    External Links:
    ISSN 0285-4821, MathReview (Peter M. Neumann), ZentralBlatt
    Referenced by:
    §24.10(ii).
    Encodings:
    BibTeX
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  • R. P. Stanley (1989) Some combinatorial properties of Jack symmetric functions. Adv. Math. 77 (1), pp. 76–115.
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    External Links:
    ISSN 0001-8708, Document, MathReview (Dennis White), ZentralBlatt
    Referenced by:
    §18.37(iii).
    Encodings:
    BibTeX
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  • O. Szász (1951) On the relative extrema of the Hermite orthogonal functions. J. Indian Math. Soc. (N.S.) 15, pp. 129–134.
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    External Links:
    MathReview (J. Todd), ZentralBlatt
    Referenced by:
    §18.14(i).
    Encodings:
    BibTeX
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  • G. Szegö (1950) On certain special sets of orthogonal polynomials. Proc. Amer. Math. Soc. 1, pp. 731–737.
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    External Links:
    ISSN 0002-9939, Document, Link, MathReview (A. C. Offord)
    Referenced by:
    §18.35(i).
    Encodings:
    BibTeX
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    25: 18.38 Mathematical Applications
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    Quadrature
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    Riemann–Hilbert Problems
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    Radon Transform
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    Group Representations
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    Dunkl Type Operators and Nonsymmetric Orthogonal Polynomials
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    26: 18.17 Integrals
    §18.17 Integrals
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    §18.17(ii) Integral Representations for Products
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    §18.17(v) Fourier Transforms
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    §18.17(vi) Laplace Transforms
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    §18.17(vii) Mellin Transforms
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    27: Bibliography G
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  • W. Gautschi (1996) Orthogonal Polynomials: Applications and Computation. In Acta Numerica, 1996, A. Iserles (Ed.), Acta Numerica, Vol. 5, pp. 45–119.
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    External Links:
    MathReview (Sven Ehrich), ZentralBlatt
    Referenced by:
    §3.5(v).
    Encodings:
    BibTeX
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  • W. Gautschi (2009) Variable-precision recurrence coefficients for nonstandard orthogonal polynomials. Numer. Algorithms 52 (3), pp. 409–418.
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    External Links:
    ISSN 1017-1398, Document, Link, MathReview Entry
    Referenced by:
    §18.39(iii), §18.40(ii).
    Encodings:
    BibTeX
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  • I. M. Gel’fand and G. E. Shilov (1964) Generalized Functions. Vol. 1: Properties and Operations. Academic Press, New York.
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    Notes:
    Translated from the Russian by Eugene Saletan. A paperbound reprinting by the same publisher appeared in 1977
    External Links:
    MathReview, ZentralBlatt
    Referenced by:
    §2.6(i).
    Encodings:
    BibTeX
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  • Z. Gong, L. Zejda, W. Dappen, and J. M. Aparicio (2001) Generalized Fermi-Dirac functions and derivatives: Properties and evaluation. Comput. Phys. Comm. 136 (3), pp. 294–309.
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    Notes:
    Double-precision Fortran, maximum accuracy 20D
    External Links:
    Document, Code, ZentralBlatt
    Referenced by:
    7th item.
    Encodings:
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  • B. Grammaticos, A. Ramani, and V. Papageorgiou (1991) Do integrable mappings have the Painlevé property?. Phys. Rev. Lett. 67 (14), pp. 1825–1828.
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    External Links:
    ISSN 0031-9007, Document, MathReview, ZentralBlatt
    Referenced by:
    §32.16.
    Encodings:
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    28: 34.7 Basic Properties: 9 ⁒ j Symbol
    §34.7 Basic Properties: 9 ⁒ j Symbol
    … β–ΊThe 9 ⁒ j symbol has symmetry properties with respect to permutation of columns, permutation of rows, and transposition of rows and columns; these relate 72 independent 9 ⁒ j symbols. … β–ΊFor further symmetry properties of the 9 ⁒ j symbol see Edmonds (1974, pp. 102–103) and Varshalovich et al. (1988, §10.4.1). … β–Ί
    §34.7(iv) Orthogonality
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    29: 18.2 General Orthogonal Polynomials
    §18.2 General Orthogonal Polynomials
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    Orthogonality on Intervals
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    Orthogonality on General Sets
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    Kernel property
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    30: Bibliography P
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  • J. B. Parkinson (1969) Optical properties of layer antiferromagnets with K 2 ⁒ NiF 4 structure. J. Phys. C: Solid State Physics 2 (11), pp. 2012–2021.
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    External Links:
    Document
    Referenced by:
    §19.35(ii).
    Encodings:
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  • P. I. Pastro (1985) Orthogonal polynomials and some q -beta integrals of Ramanujan. J. Math. Anal. Appl. 112 (2), pp. 517–540.
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    External Links:
    ISSN 0022-247X, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt
    Referenced by:
    §18.33(iv), §18.33(v).
    Encodings:
    BibTeX
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