inversion%20formula
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10 matching pages
1: Bibliography K
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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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2: Bibliography R
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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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Another proof of the triple sum formula for Wigner -symbols.
J. Math. Phys. 40 (12), pp. 6689–6691.
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3: 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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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Formulas for higher derivatives of the Riemann zeta function.
Math. Comp. 44 (169), pp. 223–232.
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Bernoulli’s power-sum formulas revisited.
Math. Gaz. 90 (518), pp. 276–279.
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4: 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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►Such sets of twelve equations include derivatives, differential equations, bisection relations, duplication relations, addition formulas (including new ones for theta functions), and pseudo-addition formulas.
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5: Bibliography C
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A quadrature formula for the Hankel transform.
Numer. Algorithms 9 (2), pp. 343–354.
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The inverse of the error function.
Pacific J. Math. 13 (2), pp. 459–470.
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Power series for inverse Jacobian elliptic functions.
Math. Comp. 77 (263), pp. 1615–1621.
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Inverse Acoustic and Electromagnetic Scattering Theory.
2nd edition, Applied Mathematical Sciences, Vol. 93, Springer-Verlag, Berlin.
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An encyclopaedia of cubature formulas.
J. Complexity 19 (3), pp. 445–453.
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6: 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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Calculation of the gamma function by Stirling’s formula.
Math. Comp. 25 (114), pp. 317–322.
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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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Gaussian Quadrature Formulas.
Prentice-Hall Inc., Englewood Cliffs, N.J..
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7: Bibliography W
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Evaluating elliptic functions and their inverses.
Comput. Math. Appl. 39 (3-4), pp. 131–136.
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Reduction formulae for products of theta functions.
J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.
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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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Recursion formulae for hypergeometric functions.
Math. Comp. 22 (102), pp. 363–373.
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Quadrature formulas for oscillatory integral transforms.
Numer. Math. 39 (3), pp. 351–360.
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8: Bibliography D
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Computation of the incomplete gamma function ratios and their inverses.
ACM Trans. Math. Software 12 (4), pp. 377–393.
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A simple sum formula for Clebsch-Gordan coefficients.
Lett. Math. Phys. 5 (3), pp. 207–211.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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Product formulas and Nicholson-type integrals for Jacobi functions. I. Summary of results.
SIAM J. Math. Anal. 9 (1), pp. 76–86.
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9: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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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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Mathieu functions of general order: Connection formulae, base functions and asymptotic formulae. I–V.
Philos. Trans. Roy. Soc. London Ser. A 301, pp. 75–162.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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10: Bibliography P
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An asymptotic formula for the incomplete gamma function.
Ž. Vyčisl. Mat. i Mat. Fiz. 5, pp. 118–121 (Russian).
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations.
J. Quantit. Spec. and Rad. Trans. 62 (4), pp. 389–395.
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Recurrence formulas for Coulomb wave functions.
Physical Rev. (2) 72 (7), pp. 626–627.
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Integrals and Series: Inverse Laplace Transforms, Vol. 5.
Gordon and Breach Science Publishers, New York.
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