relation to Lamé equation
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11—19 of 19 matching pages
11: Bibliography W
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Asymptotics of orthogonal polynomials via recurrence relations.
Anal. Appl. (Singap.) 10 (2), pp. 215–235.
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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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Some useful integrals of
and related integrals.
Optica Acta 14 (3), pp. 317–322.
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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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Computation with Recurrence Relations.
Pitman, Boston, MA.
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12: 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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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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On the rational solutions of the second Painlevé equation.
Differ. Uravn. 1 (1), pp. 79–81 (Russian).
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13: 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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14: Bibliography B
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An Introduction to Linear Difference Equations.
Dover Publications Inc., New York.
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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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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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Concerning the zeros of some functions related to Bessel functions.
J. Mathematical Phys. 10 (9), pp. 1729–1744.
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15: Bibliography R
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Composite approximations to the solutions of the Orr-Sommerfeld equation.
Studies in Appl. Math. 51, pp. 341–368.
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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. I. Plane Couette flow.
Studies in Appl. Math. 53, pp. 91–110.
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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. II. The general theory.
Studies in Appl. Math. 53, pp. 217–224.
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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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The similarity solution for the Korteweg-de Vries equation and the related Painlevé transcendent.
Proc. Roy. Soc. London Ser. A 361, pp. 265–275.
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16: Bibliography M
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On reducing the Heun equation to the hypergeometric equation.
J. Differential Equations 213 (1), pp. 171–203.
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Connection between quantum systems involving the fourth Painlevé transcendent and -step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial.
J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..
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On a class of algebraic solutions to the Painlevé VI equation, its determinant formula and coalescence cascade.
Funkcial. Ekvac. 46 (1), pp. 121–171.
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Picard and Chazy solutions to the Painlevé VI equation.
Math. Ann. 321 (1), pp. 157–195.
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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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17: 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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Numerical calculation of singular integrals related to Hankel transform.
Comput. Math. Appl. 21 (2-3), pp. 87–94.
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On a unified approach to transformations and elementary solutions of Painlevé equations.
J. Math. Phys. 23 (11), pp. 2033–2042.
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From continuous to discrete Painlevé equations.
J. Math. Anal. Appl. 180 (2), pp. 342–360.
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Application of the -function theory of Painlevé equations to random matrices: PIV, PII and the GUE.
Comm. Math. Phys. 219 (2), pp. 357–398.
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18: Bibliography D
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Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions.
Proc. Roy. Soc. London Ser. A 440, pp. 37–54.
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Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function.
Proc. Roy. Soc. London Ser. A 452, pp. 1331–1349.
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Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions.
Stud. Appl. Math. 107 (3), pp. 293–323.
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Convergent expansions for solutions of linear ordinary differential equations having a simple pole, with an application to associated Legendre functions.
Stud. Appl. Math. 113 (3), pp. 245–270.
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Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point.
Anal. Appl. (Singap.) 12 (4), pp. 385–402.
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19: Bibliography H
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Sums with cylindrical functions that reduce to the probability function and to related functions.
Bul. Akad. Shtiintse RSS Moldoven. 1978 (3), pp. 80–84, 95 (Russian).
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Lamé polynomials of large order.
SIAM J. Math. Anal. 8 (5), pp. 800–842.
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Poncelet Polygons and the Painlevé Equations.
In Geometry and Analysis (Bombay, 1992), Ramanan (Ed.),
pp. 151–185.
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Estimates of the stability intervals for Hill’s equation.
Proc. Amer. Math. Soc. 14 (6), pp. 930–932.
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Differential Equations: A Modern Approach.
Holt, Rinehart and Winston, New York.
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