linear%20functionals
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1: Bibliography D
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Complex zeros of linear combinations of spherical Bessel functions and their derivatives.
SIAM J. Math. Anal. 4 (1), pp. 128–133.
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Theta functions and non-linear equations.
Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).
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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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2: Bibliography G
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The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals.
Ann. of Math. (2) 48 (4), pp. 785–826.
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The Computation of Special Functions by Linear Difference Equations.
In Advances in Difference Equations (Veszprém, 1995), S. Elaydi, I. Győri, and G. Ladas (Eds.),
pp. 213–243.
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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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Linear Differential Equations and Group Theory from Riemann to Poincaré.
2nd edition, Birkhäuser Boston Inc., Boston, MA.
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Kinetic theory of linear shear flow.
Phys. Fluids 1 (3), pp. 215–224.
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3: William P. Reinhardt
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►He has recently carried out research on non-linear dynamics of Bose–Einstein condensates that served to motivate his interest in elliptic functions.
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►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
4: Bibliography W
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Linear difference equations with transition points.
Math. Comp. 74 (250), pp. 629–653.
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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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Linear Turning Point Theory.
Applied Mathematical Sciences No. 54, Springer-Verlag, New York.
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Linear and Nonlinear Waves.
John Wiley & Sons, New York.
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Asymptotics of linear recurrences.
Anal. Appl. (Singap.) 12 (4), pp. 463–484.
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5: 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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Linear algebra done right.
Third edition, Undergraduate Texts in Mathematics, Springer, Cham.
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6: Bibliography K
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Quasi-linear Stokes phenomenon for the Painlevé first equation.
J. Phys. A 37 (46), pp. 11149–11167.
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Linear convergence and the bisection algorithm.
Amer. Math. Monthly 93 (1), pp. 48–51.
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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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An algorithm for solving second order linear homogeneous differential equations.
J. Symbolic Comput. 2 (1), pp. 3–43.
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7: Bibliography M
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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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David Wright’s software package for .NET programming language
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On the choice of standard solutions for a homogeneous linear differential equation of the second order.
Quart. J. Mech. Appl. Math. 3 (2), pp. 225–235.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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8: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Non-linear integral equations for Heun functions.
Proc. Edinburgh Math. Soc. (2) 16, pp. 281–289.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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9: Bibliography O
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Hyperasymptotic solutions of second-order linear differential equations. I.
Methods Appl. Anal. 2 (2), pp. 173–197.
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On the calculation of Stokes multipliers for linear differential equations of the second order.
Methods Appl. Anal. 2 (3), pp. 348–367.
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On the asymptotic and numerical solution of linear ordinary differential equations.
SIAM Rev. 40 (3), pp. 463–495.
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Hyperasymptotic solutions of second-order linear differential equations. II.
Methods Appl. Anal. 2 (2), pp. 198–211.
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Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one.
Proc. Roy. Soc. London Ser. A 454, pp. 1–29.
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10: Bibliography B
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Transcendental Functions Satisfying Nonhomogeneous Linear Differential Equations.
The Macmillan Co., New York.
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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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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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Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-order Differential Equations: The Simple Pole Case.
In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.),
Lecture Notes in Pure and Applied Mathematics, Vol. 124, pp. 53–73.
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