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summability methods for integrals


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1: 1.15 Summability Methods
§1.15(iv) Definitions for Integrals
Abel Summability
Cesàro Summability
§1.15(vi) Fractional Integrals
2: Bibliography W
  • P. L. Walker (2009) The distribution of the zeros of Jacobian elliptic functions with respect to the parameter k . Comput. Methods Funct. Theory 9 (2), pp. 579–591.
  • J. A. Wheeler (1937) Wave functions for large arguments by the amplitude-phase method. Phys. Rev. 52, pp. 1123–1127.
  • A. D. Wheelon (1968) Tables of Summable Series and Integrals Involving Bessel Functions. Holden-Day, San Francisco, CA.
  • R. Wong and M. Wyman (1974) The method of Darboux. J. Approximation Theory 10 (2), pp. 159–171.
  • R. Wong and Y. Zhao (2005) On a uniform treatment of Darboux’s method. Constr. Approx. 21 (2), pp. 225–255.
  • 3: Bibliography S
  • D. Schmidt and G. Wolf (1979) A method of generating integral relations by the simultaneous separability of generalized Schrödinger equations. SIAM J. Math. Anal. 10 (4), pp. 823–838.
  • I. Shavitt and M. Karplus (1965) Gaussian-transform method for molecular integrals. I. Formulation for energy integrals. J. Chem. Phys. 43 (2), pp. 398–414.
  • B. Simon (1982) Large orders and summability of eigenvalue perturbation theory: A mathematical overview. Int. J. Quantum Chem. 21, pp. 3–25.
  • I. A. Stegun and R. Zucker (1974) Automatic computing methods for special functions. II. The exponential integral E n ( x ) . J. Res. Nat. Bur. Standards Sect. B 78B, pp. 199–216.
  • I. A. Stegun and R. Zucker (1976) Automatic computing methods for special functions. III. The sine, cosine, exponential integrals, and related functions. J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 291–311.
  • 4: Bibliography F
  • S. Fempl (1960) Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
  • H. E. Fettis (1970) On the reciprocal modulus relation for elliptic integrals. SIAM J. Math. Anal. 1 (4), pp. 524–526.
  • W. B. Ford (1960) Studies on Divergent Series and Summability & The Asymptotic Developments of Functions Defined by Maclaurin Series. Chelsea Publishing Co., New York.
  • C. H. Franke (1965) Numerical evaluation of the elliptic integral of the third kind. Math. Comp. 19 (91), pp. 494–496.
  • B. R. Frieden (1971) Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions. In Progress in Optics, E. Wolf (Ed.), Vol. 9, pp. 311–407.