analytic%20functions
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11—19 of 19 matching pages
11: 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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Jacobi polynomials. II. An analytic proof of the product formula.
SIAM J. Math. Anal. 5, pp. 125–137.
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Jacobi polynomials. III. An analytic proof of the addition formula.
SIAM. J. Math. Anal. 6, pp. 533–543.
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Bessel Functions and their Applications.
Analytical Methods and Special Functions, Vol. 8, Taylor & Francis Ltd., London-New York.
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12: Tom M. Apostol
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►Apostol was born on August 20, 1923.
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►He was internationally known for his textbooks on calculus, analysis, and analytic number theory, which have been translated into five languages, and for creating Project
MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects.
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►Apostol served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions.
13: 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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Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable.
2nd edition, McGraw-Hill Book Co., New York.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Hypergeometric Functions and Elliptic Integrals.
In Current Topics in Analytic Function Theory, H. M. Srivastava and S. Owa (Eds.),
pp. 48–85.
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14: 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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The analyticity of Jacobian functions with respect to the parameter
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Proc. Roy. Soc. London Ser A 459, pp. 2569–2574.
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Analytic Theory of Continued Fractions.
D. Van Nostrand Company, Inc., New York.
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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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A Treatise on the Analytical Dynamics of Particles and Rigid Bodies.
4th edition, Cambridge University Press, Cambridge.
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15: 25.11 Hurwitz Zeta Function
§25.11 Hurwitz Zeta Function
►§25.11(i) Definition
… ►As a function of , with () fixed, is analytic in the half-plane . The Riemann zeta function is a special case: … ►§25.11(ii) Graphics
…16: Bibliography R
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On the partition function p(n).
Proc. London Math. Soc. (2) 43 (4), pp. 241–254.
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Topics in Analytic Number Theory.
Springer-Verlag, New York.
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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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Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function.
Mathematics 9 (16).
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17: 18.39 Applications in the Physical Sciences
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►Below we consider two potentials with analytically known eigenfunctions and eigenvalues where the spectrum is entirely point, or discrete, with all eigenfunctions being and forming a complete set.
Also presented are the analytic solutions for the , bound state, eigenfunctions and eigenvalues of the Morse oscillator which also has analytically known non-normalizable continuum eigenfunctions, thus providing an example of a mixed spectrum.
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1D Quantum Systems with Analytically Known Stationary States
… ►Other Analytically Solved Schrödinger Equations
… ►The discrete variable representations (DVR) analysis is simplest when based on the classical OP’s with their analytically known recursion coefficients (Table 3.5.17_5), or those non-classical OP’s which have analytically known recursion coefficients, making stable computation of the and , from the J-matrix as in §3.5(vi), straightforward. …18: Bibliography P
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Tables of Digamma and Trigamma Functions.
In Tracts for Computers, No. 1, K. Pearson (Ed.),
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Exponential asymptotics of the Mittag-Leffler function.
Proc. Roy. Soc. London Ser. A 458, pp. 3041–3052.
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Tables of the Incomplete Beta-function.
2nd edition, Published for the Biometrika Trustees at the Cambridge
University Press, Cambridge.
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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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19: Bibliography C
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Analytical solution of a model for complex food webs.
Phys. Rev. E 65 (3), pp. (030901–1)–(030901–4).
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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The analyticity of cross-product Bessel function zeros.
Proc. Cambridge Philos. Soc. 62, pp. 215–226.
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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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