relation to Lamé functions
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11—20 of 22 matching pages
11: Bibliography B
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Orthogonality relations for the associated Legendre functions of imaginary order.
Integral Transforms Spec. Funct. 24 (4), pp. 331–337.
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Tables Relating to the Radial Mathieu Functions. Vol. 1: Functions of the First Kind.
U.S. Government Printing Office, Washington, D.C..
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Tables Relating to the Radial Mathieu Functions. Vol. 2: Functions of the Second Kind.
U.S. Government Printing Office, Washington, D.C..
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Concerning the zeros of some functions related to Bessel functions.
J. Mathematical Phys. 10 (9), pp. 1729–1744.
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Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems.
J. Phys. A 34 (40), pp. 8199–8220.
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12: 29.14 Orthogonality
§29.14 Orthogonality
►Lamé polynomials are orthogonal in two ways. First, the orthogonality relations (29.3.19) apply; see §29.12(i). Secondly, the system of functions …is orthogonal and complete with respect to the inner product …13: Bibliography S
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Lamé polynomial solutions to some elliptic crack and punch problems.
Internat. J. Engrg. Sci. 16 (8), pp. 551–563.
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On integral representations for Lamé and other special functions.
SIAM J. Math. Anal. 11 (4), pp. 702–723.
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Structure of avoided crossings for eigenvalues related to equations of Heun’s class.
J. Phys. A 30 (2), pp. 673–687.
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The expansion of Lamé functions into series of associated Legendre functions of the second kind.
Proc. Cambridge Philos. Soc. 62, pp. 441–452.
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Integral equations and relations for Lamé functions and ellipsoidal wave functions.
Proc. Cambridge Philos. Soc. 64, pp. 113–126.
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14: Bibliography M
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Crossing symmetric expansions of physical scattering amplitudes: The group and Lamé functions.
J. Mathematical Phys. 12, pp. 281–293.
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Chebyshev expansions for modified Struve and related functions.
Math. Comp. 60 (202), pp. 735–747.
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Uniform computation of the error function and other related functions.
Math. Comp. 25 (114), pp. 339–344.
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Evaluation of complex logarithms and related functions.
SIAM J. Numer. Anal. 18 (4), pp. 744–750.
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A new symmetry related to
for classical basic hypergeometric series.
Adv. in Math. 57 (1), pp. 71–90.
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15: 28.34 Methods of Computation
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(b)
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(c)
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(f)
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§28.34(iv) Modified Mathieu Functions
►For the modified functions we have: …16: Bibliography V
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An integral transform involving Heun functions and a related eigenvalue problem.
SIAM J. Math. Anal. 17 (3), pp. 688–703.
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Airy Functions and Applications to Physics.
Second edition, Imperial College Press, London.
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Integral relations for Lamé functions.
SIAM J. Math. Anal. 13 (6), pp. 978–987.
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Integral representations for products of Lamé functions by use of fundamental solutions.
SIAM J. Math. Anal. 15 (3), pp. 559–569.
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Four remarks on eigenvalues of Lamé’s equation.
Anal. Appl. (Singap.) 2 (2), pp. 161–175.
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17: Bibliography W
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Elliptic Functions According to Eisenstein and Kronecker.
Classics in Mathematics, Springer-Verlag, Berlin.
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Rapid approximation to the Voigt/Faddeeva function and its derivatives.
J. Quant. Spect. and Rad. Transfer 62 (1), pp. 29–48.
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Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials.
Ph.D. Thesis, University of Wisconsin, Madison, WI.
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Some explicit Padé approximants for the function
and a related quadrature formula involving Bessel functions.
SIAM J. Math. Anal. 16 (4), pp. 887–895.
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18: Bibliography I
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The periodic Lamé functions.
Proc. Roy. Soc. Edinburgh 60, pp. 47–63.
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Further investigations into the periodic Lamé functions.
Proc. Roy. Soc. Edinburgh 60, pp. 83–99.
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Special Functions, -Series and Related Topics.
Fields Institute Communications, Vol. 14, American Mathematical Society, Providence, RI.
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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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Bounds for the small real and purely imaginary zeros of Bessel and related functions.
Methods Appl. Anal. 2 (1), pp. 1–21.
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19: Bibliography R
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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (4), pp. 91.
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On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators.
Z. Angew. Math. Mech. 78 (1), pp. 66–72.
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Some Applications of the Lamé Function Solutions of the Linearised Supersonic Flow Equations.
Technical Reports and Memoranda
Technical Report 2865, Aeronautical Research Council (Great Britain).
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Elliptic and modular functions from Gauss to Dedekind to Hecke.
Cambridge University Press, Cambridge.
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On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media.
In Differential Operators and Related Topics, Vol. I (Odessa,
1997),
Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.
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20: Bibliography F
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The Lamé wave equation.
Uspekhi Mat. Nauk 44 (1(265)), pp. 123–144, 248 (Russian).
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On the reciprocal modulus relation for elliptic integrals.
SIAM J. Math. Anal. 1 (4), pp. 524–526.
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Numerical calculation of singular integrals related to Hankel transform.
Comput. Math. Appl. 21 (2-3), pp. 87–94.
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Guide to tables of elliptic functions.
Math. Tables and Other Aids to Computation 3 (24), pp. 229–281.
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Polynomial relations in the Heisenberg algebra.
J. Math. Phys. 35 (11), pp. 6144–6149.
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