Legendre%20polynomials
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1: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials.
Mem. Amer. Math. Soc. 54 (319), pp. iv+55.
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2: Bibliography L
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Essai sur la Théorie des Nombres.
2nd edition, Courcier, Paris.
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Traité des fonctions elliptiques et des intégrales Eulériennes.
Huzard-Courcier, Paris.
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Algorithm 567: Extended-range arithmetic and normalized Legendre polynomials [A1], [C1].
ACM Trans. Math. Software 7 (1), pp. 141–146.
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3: Software Index
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4: 18.5 Explicit Representations
§18.5 Explicit Representations
… ►For corresponding formulas for Chebyshev, Legendre, and the Hermite polynomials apply (18.7.3)–(18.7.6), (18.7.9), and (18.7.11). … ► … ►Legendre
… ►5: 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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Error bounds for a uniform asymptotic expansion of the Legendre function
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SIAM J. Math. Anal. 21 (2), pp. 523–535.
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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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6: 19.36 Methods of Computation
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►Legendre’s integrals can be computed from symmetric integrals by using the relations in §19.25(i).
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►(In Legendre’s notation the modulus approaches 0 or 1.)
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►For computation of Legendre’s integral of the third kind, see Abramowitz and Stegun (1964, §§17.7 and 17.8, Examples 15, 17, 19, and 20).
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►For series expansions of Legendre’s integrals see §19.5.
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7: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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On the Associated Legendre Polynomials.
In Orthogonal Expansions and their Continuous Analogues (Proc.
Conf., Edwardsville, Ill., 1967),
pp. 43–50.
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A generalisation of the Legendre polynomial.
Proc. London Math. Soc. (2) 3 (3), pp. 111–123.
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Tables of Normalized Associated Legendre Polynomials.
Pergamon Press, The Macmillan Co., Oxford-New York.
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Associated Legendre polynomials, ordinary and modified spherical harmonics.
Comput. Phys. Comm. 5 (5), pp. 390–394.
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8: Bibliography V
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Generalized Associated Legendre Functions and their Applications.
World Scientific Publishing Co. Inc., Singapore.
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Expansions in products of Heine-Stieltjes polynomials.
Constr. Approx. 15 (4), pp. 467–480.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials.
J. Comput. Appl. Math. 213 (2), pp. 488–500.
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9: Bibliography G
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Algorithm 259: Legendre functions for arguments larger than one.
Comm. ACM 8 (8), pp. 488–492.
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Integrals of three Bessel functions and Legendre functions. I.
J. Math. Phys. 26 (4), pp. 633–644.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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10: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Multi-Integral Representations for Associated Legendre and Ferrers Functions.
Symmetry 12 (10).
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On parameter differentiation for integral representations of associated Legendre functions.
SIGMA Symmetry Integrability Geom. Methods Appl. 7, pp. Paper 050, 16.
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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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