About the Project

relation%20to%20associated%20Legendre%20functions

AdvancedHelp

(0.010 seconds)

8 matching pages

1: Bibliography B
  • S. L. Belousov (1962) Tables of Normalized Associated Legendre Polynomials. Pergamon Press, The Macmillan Co., Oxford-New York.
  • S. Bielski (2013) Orthogonality relations for the associated Legendre functions of imaginary order. Integral Transforms Spec. Funct. 24 (4), pp. 331–337.
  • G. Blanch and D. S. Clemm (1962) Tables Relating to the Radial Mathieu Functions. Vol. 1: Functions of the First Kind. U.S. Government Printing Office, Washington, D.C..
  • G. Blanch and D. S. Clemm (1965) Tables Relating to the Radial Mathieu Functions. Vol. 2: Functions of the Second Kind. U.S. Government Printing Office, Washington, D.C..
  • S. Bochner (1952) 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.
  • 2: Bibliography V
  • G. Valent (1986) An integral transform involving Heun functions and a related eigenvalue problem. SIAM J. Math. Anal. 17 (3), pp. 688–703.
  • J. Van Deun and R. Cools (2008) Integrating products of Bessel functions with an additional exponential or rational factor. Comput. Phys. Comm. 178 (8), pp. 578–590.
  • N. Virchenko and I. Fedotova (2001) Generalized Associated Legendre Functions and their Applications. World Scientific Publishing Co. Inc., Singapore.
  • H. Volkmer (1982) Integral relations for Lamé functions. SIAM J. Math. Anal. 13 (6), pp. 978–987.
  • H. Volkmer (2004a) Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.
  • 3: Software Index
  • Open Source Collections and Systems.

    These are collections of software (e.g. libraries) or interactive systems of a somewhat broad scope. Contents may be adapted from research software or may be contributed by project participants who donate their services to the project. The software is made freely available to the public, typically in source code form. While formal support of the collection may not be provided by its developers, within active projects there is often a core group who donate time to consider bug reports and make updates to the collection.

  • Software Associated with Books.

    An increasing number of published books have included digital media containing software described in the book. Often, the collection of software covers a fairly broad area. Such software is typically developed by the book author. While it is not professionally packaged, it often provides a useful tool for readers to experiment with the concepts discussed in the book. The software itself is typically not formally supported by its authors.

  • Commercial Software.

    Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

  • Computer Physics Communications Program Library

    Software associated with papers published in the journal Computer Physics Communications.

  • Guide to Available Mathematical Software

    A cross index of mathematical software in use at NIST.

  • 4: Bibliography
  • V. S. Adamchik and H. M. Srivastava (1998) Some series of the zeta and related functions. Analysis (Munich) 18 (2), pp. 131–144.
  • J. C. Adams and P. N. Swarztrauber (1997) SPHEREPACK 2.0: A Model Development Facility. NCAR Technical Note Technical Report TN-436-STR, National Center for Atmospheric Research.
  • D. E. Amos (1989) Repeated integrals and derivatives of K Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.
  • T. M. Apostol and T. H. Vu (1984) Dirichlet series related to the Riemann zeta function. J. Number Theory 19 (1), pp. 85–102.
  • F. M. Arscott (1964a) Integral equations and relations for Lamé functions. Quart. J. Math. Oxford Ser. (2) 15, pp. 103–115.
  • 5: Bibliography C
  • W. J. Cody (1991) Performance evaluation of programs related to the real gamma function. ACM Trans. Math. Software 17 (1), pp. 46–54.
  • H. S. Cohl and R. S. Costas-Santos (2020) Multi-Integral Representations for Associated Legendre and Ferrers Functions. Symmetry 12 (10).
  • H. S. Cohl (2010) Derivatives with respect to the degree and order of associated Legendre functions for | z | > 1 using modified Bessel functions. Integral Transforms Spec. Funct. 21 (7-8), pp. 581–588.
  • H. S. Cohl (2011) On parameter differentiation for integral representations of associated Legendre functions. SIGMA Symmetry Integrability Geom. Methods Appl. 7, pp. Paper 050, 16.
  • M. Colman, A. Cuyt, and J. Van Deun (2011) Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
  • 6: Bibliography S
  • B. I. Schneider, J. Segura, A. Gil, X. Guan, and K. Bartschat (2010) A new Fortran 90 program to compute regular and irregular associated Legendre functions. Comput. Phys. Comm. 181 (12), pp. 2091–2097.
  • J. Segura and A. Gil (1999) Evaluation of associated Legendre functions off the cut and parabolic cylinder functions. Electron. Trans. Numer. Anal. 9, pp. 137–146.
  • R. Szmytkowski (2009) On the derivative of the associated Legendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order). J. Math. Chem. 46 (1), pp. 231–260.
  • R. Szmytkowski (2011) On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order). J. Math. Chem. 49 (7), pp. 1436–1477.
  • R. Szmytkowski (2012) On parameter derivatives of the associated Legendre function of the first kind (with applications to the construction of the associated Legendre function of the second kind of integer degree and order). J. Math. Anal. Appl. 386 (1), pp. 332–342.
  • 7: Bibliography O
  • O. M. Ogreid and P. Osland (1998) Summing one- and two-dimensional series related to the Euler series. J. Comput. Appl. Math. 98 (2), pp. 245–271.
  • J. Oliver (1977) An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series. J. Inst. Math. Appl. 20 (3), pp. 379–391.
  • F. W. J. Olver and J. M. Smith (1983) Associated Legendre functions on the cut. J. Comput. Phys. 51 (3), pp. 502–518.
  • F. W. J. Olver (Ed.) (1960) Bessel Functions. Part III: Zeros and Associated Values. Royal Society Mathematical Tables, Volume 7, Cambridge University Press, Cambridge-New York.
  • F. W. J. Olver (1975b) Legendre functions with both parameters large. Philos. Trans. Roy. Soc. London Ser. A 278, pp. 175–185.
  • 8: Bibliography G
  • W. Gautschi (1959b) Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. Phys. 38 (1), pp. 77–81.
  • W. Gautschi (1984) Questions of Numerical Condition Related to Polynomials. In Studies in Numerical Analysis, G. H. Golub (Ed.), pp. 140–177.
  • A. Gervois and H. Navelet (1985a) Integrals of three Bessel functions and Legendre functions. I. J. Math. Phys. 26 (4), pp. 633–644.
  • A. Gil, J. Segura, and N. M. Temme (2014) Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
  • W. Groenevelt (2007) Fourier transforms related to a root system of rank 1. Transform. Groups 12 (1), pp. 77–116.