Abel%20summability
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1: 1.15 Summability Methods
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Abel Summability
… ►Abel Means
… ►Abel Summability
► is Abel summable to , or … ►If converges and equals , then the integral is Abel and Cesàro summable to . …2: 22.18 Mathematical Applications
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§22.18(iv) Elliptic Curves and the Jacobi–Abel Addition Theorem
… ►For any two points and on this curve, their sum , always a third point on the curve, is defined by the Jacobi–Abel addition law …a construction due to Abel; see Whittaker and Watson (1927, pp. 442, 496–497). …3: 20 Theta Functions
Chapter 20 Theta Functions
…4: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Abelian Functions: Abel’s Theorem and the Allied Theory of Theta Functions.
Cambridge University Press, Cambridge.
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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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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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5: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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Studies on Divergent Series and Summability & The Asymptotic Developments of Functions Defined by Maclaurin Series.
Chelsea Publishing Co., New York.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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6: 2.10 Sums and Sequences
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►Another version is the Abel–Plana formula:
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(c)
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The first infinite integral in (2.10.2) converges.
7: Bibliography W
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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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Tables of Summable Series and Integrals Involving Bessel Functions.
Holden-Day, San Francisco, CA.
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8: 8 Incomplete Gamma and Related
Functions
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9: 28 Mathieu Functions and Hill’s Equation
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10: 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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Large orders and summability of eigenvalue perturbation theory: A mathematical overview.
Int. J. Quantum Chem. 21, pp. 3–25.
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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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