Jacobi%20function
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1: 22.3 Graphics
2: 20.11 Generalizations and Analogs
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►This is Jacobi’s inversion problem of §20.9(ii).
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►Each provides an extension of Jacobi’s inversion problem.
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§20.11(iv) Theta Functions with Characteristics
… ►For , , and , define twelve combined theta functions by …3: 20.7 Identities
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20.7.34
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4: 20.10 Integrals
§20.10 Integrals
►§20.10(i) Mellin Transforms with respect to the Lattice Parameter
… ►Here again denotes the Riemann zeta function (§25.2). … ►§20.10(ii) Laplace Transforms with respect to the Lattice Parameter
… ►For corresponding results for argument derivatives of the theta functions see Erdélyi et al. (1954a, pp. 224–225) or Oberhettinger and Badii (1973, p. 193). …5: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Cyclic identities for Jacobi elliptic and related functions.
J. Math. Phys. 44 (4), pp. 1822–1841.
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Connecting Jacobi elliptic functions with different modulus parameters.
Pramana 63 (5), pp. 921–936.
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Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups.
In Special Functions: Group Theoretical Aspects and Applications,
pp. 1–85.
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6: Bibliography B
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The generating function of Jacobi polynomials.
J. London Math. Soc. 13, pp. 8–12.
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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A short table of the functions
, from to
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Phil. Mag. Series 7 20, pp. 343–347.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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7: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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A uniform asymptotic expansion of the Jacobi polynomials with error bounds.
Canad. J. Math. 37 (5), pp. 979–1007.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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8: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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A Bernstein-type inequality for the Jacobi polynomial.
Proc. Amer. Math. Soc. 121 (3), pp. 703–709.
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Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems.
SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 042, 26.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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9: Bibliography I
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Theta Functions.
Springer-Verlag, New York.
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Tables of the elliptic cylinder functions.
Proc. Roy. Soc. Edinburgh Sect. A 52, pp. 355–433.
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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Two families of orthogonal polynomials related to Jacobi polynomials.
Rocky Mountain J. Math. 21 (1), pp. 359–375.
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Asymptotics of the Askey-Wilson and -Jacobi polynomials.
SIAM J. Math. Anal. 17 (6), pp. 1475–1482.
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10: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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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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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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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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