Pringsheim%20theorem%20for%20continued%20fractions
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11—20 of 313 matching pages
11: 36 Integrals with Coalescing Saddles
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12: Gergő Nemes
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►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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13: Wolter Groenevelt
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►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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14: 33.24 Tables
15: 3.8 Nonlinear Equations
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►This is an iterative method for real twice-continuously differentiable, or complex analytic, functions:
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►Initial approximations to the zeros can often be found from asymptotic or other approximations to , or by application of the phase principle or Rouché’s theorem; see §1.10(iv).
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►Consider and .
We have and .
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16: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Hill’s Equation.
Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney.
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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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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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17: 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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Theorems on generalized Dedekind sums.
Pacific J. Math. 2 (1), pp. 1–9.
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18: William P. Reinhardt
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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.
19: Bibliography R
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Normal limit theorems for symmetric random matrices.
Probab. Theory Related Fields 112 (3), pp. 411–423.
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A code to calculate (high order) Bessel functions based on the continued fractions method.
Comput. Phys. Comm. 76 (3), pp. 381–388.
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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13 Lectures on Fermat’s Last Theorem.
Springer-Verlag, New York.
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Dawson’s integral and the sampling theorem.
Computers in Physics 3 (2), pp. 85–87.
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20: Bibliography C
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The Staudt-Clausen theorem.
Math. Mag. 34, pp. 131–146.
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Short proofs of three theorems on elliptic integrals.
SIAM J. Math. Anal. 9 (3), pp. 524–528.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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