for%20inverse%20function
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1—10 of 18 matching pages
1: Bibliography C
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The inverse of the error function.
Pacific J. Math. 13 (2), pp. 459–470.
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Jacobian elliptic functions as inverses of an integral.
J. Comput. Appl. Math. 174 (2), pp. 355–359.
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Power series for inverse Jacobian elliptic functions.
Math. Comp. 77 (263), pp. 1615–1621.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Inverse Acoustic and Electromagnetic Scattering Theory.
2nd edition, Applied Mathematical Sciences, Vol. 93, Springer-Verlag, Berlin.
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2: 18.40 Methods of Computation
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§18.40(ii) The Classical Moment Problem
… ►Stieltjes Inversion via (approximate) Analytic Continuation
… ►Histogram Approach
… ►Derivative Rule Approach
… ►The example chosen is inversion from the for the weight function for the repulsive Coulomb–Pollaczek, RCP, polynomials of (18.39.50). …3: Bibliography I
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Theta Functions.
Springer-Verlag, New York.
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Tables of the elliptic cylinder functions.
Proc. Roy. Soc. Edinburgh Sect. A 52, pp. 355–433.
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The periodic Lamé functions.
Proc. Roy. Soc. Edinburgh 60, pp. 47–63.
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.
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4: 10.73 Physical Applications
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►See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25).
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►More recently, Bessel functions appear in the inverse problem in wave propagation, with applications in medicine, astronomy, and acoustic imaging.
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§10.73(iii) Kelvin Functions
… ►§10.73(iv) Bickley Functions
…5: Bibliography K
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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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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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Quantum Inverse Scattering Method and Correlation Functions.
Cambridge University Press, Cambridge.
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6: Bibliography
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Solitons, Nonlinear Evolution Equations and Inverse Scattering.
London Mathematical Society Lecture Note Series, Vol. 149, Cambridge University Press, Cambridge.
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Solitons and the Inverse Scattering Transform.
SIAM Studies in Applied Mathematics, Vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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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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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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7: Bibliography R
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Elliptic Functions, Theta Functions, and Riemann Surfaces.
The Williams & Wilkins Co., Baltimore, MD.
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Fourier analysis and signal processing by use of the Möbius inversion formula.
IEEE Trans. Acoustics, Speech, Signal Processing 38, pp. 458–470.
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Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.
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Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function.
Mathematics 9 (16).
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8: 20.11 Generalizations and Analogs
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►If both are positive, then allows inversion of its arguments as a modular transformation (compare (23.15.3) and (23.15.4)):
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►This is Jacobi’s inversion problem of §20.9(ii).
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►Each provides an extension of Jacobi’s inversion problem.
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§20.11(iv) Theta Functions with Characteristics
…9: 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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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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On the calculation of the inverse of the error function.
Math. Comp. 22 (101), pp. 144–158.
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10: 12.11 Zeros
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