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modified expansions in terms of elementary functions

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11: Bibliography G
  • R. E. Gaunt (2014) Inequalities for modified Bessel functions and their integrals. J. Math. Anal. Appl. 420 (1), pp. 373–386.
  • W. Gautschi and J. Slavik (1978) On the computation of modified Bessel function ratios. Math. Comp. 32 (143), pp. 865–875.
  • W. Gautschi (1959b) Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. Phys. 38 (1), pp. 77–81.
  • A. Gil, J. Segura, and N. M. Temme (2003a) Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion. J. Comput. Appl. Math. 153 (1-2), pp. 225–234.
  • GSL (free C library) GNU Scientific Library The GNU Project.
  • 12: Bibliography M
  • A. J. MacLeod (1993) Chebyshev expansions for modified Struve and related functions. Math. Comp. 60 (202), pp. 735–747.
  • T. M. MacRobert (1967) Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications. 3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.
  • X. Merrheim (1994) The computation of elementary functions in radix 2 p . Computing 53 (3-4), pp. 219–232.
  • H. J. W. Müller (1966b) Asymptotic expansions of ellipsoidal wave functions in terms of Hermite functions. Math. Nachr. 32, pp. 49–62.
  • J. Muller (1997) Elementary Functions: Algorithms and Implementation. Birkhäuser Boston Inc., Boston, MA.
  • 13: Bibliography S
  • H. Shanker (1939) On the expansion of the parabolic cylinder function in a series of the product of two parabolic cylinder functions. J. Indian Math. Soc. (N. S.) 3, pp. 226–230.
  • A. Sharples (1971) Uniform asymptotic expansions of modified Mathieu functions. J. Reine Angew. Math. 247, pp. 1–17.
  • T. Shiota (1986) Characterization of Jacobian varieties in terms of soliton equations. Invent. Math. 83 (2), pp. 333–382.
  • D. M. Smith (1989) Efficient multiple-precision evaluation of elementary functions. Math. Comp. 52 (185), pp. 131–134.
  • K. Soni (1980) Exact error terms in the asymptotic expansion of a class of integral transforms. I. Oscillatory kernels. SIAM J. Math. Anal. 11 (5), pp. 828–841.
  • 14: Bibliography R
  • Ju. M. Rappoport (1979) Tablitsy modifitsirovannykh funktsii Besselya K 1 2 + i β ( x ) . “Nauka”, Moscow (Russian).
  • M. Razaz and J. L. Schonfelder (1980) High precision Chebyshev expansions for Airy functions and their derivatives. Technical report University of Birmingham Computer Centre.
  • R. Reynolds and A. Stauffer (2021) Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function. Mathematics 9 (16).
  • M. D. Rogers (2005) Partial fractions expansions and identities for products of Bessel functions. J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
  • K. H. Rosen (2004) Elementary Number Theory and its Applications. 5th edition, Addison-Wesley, Reading, MA.