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1: 4 Elementary Functions
Chapter 4 Elementary Functions
2: Bibliography X
  • G. L. Xu and J. K. Li (1994) Variable precision computation of elementary functions. J. Numer. Methods Comput. Appl. 15 (3), pp. 161–171 (Chinese).
  • 3: 17.17 Physical Applications
    See Kassel (1995). …
    4: Karl Dilcher
    Dilcher’s research interests include classical analysis, special functions, and elementary, combinatorial, and computational number theory. …
    5: Ranjan Roy
    6: 19.36 Methods of Computation
    When the differences are moderately small, the iteration is stopped, the elementary symmetric functions of certain differences are calculated, and a polynomial consisting of a fixed number of terms of the sum in (19.19.7) is evaluated. …
    19.36.1 1 - 1 10 E 2 + 1 14 E 3 + 1 24 E 2 2 - 3 44 E 2 E 3 - 5 208 E 2 3 + 3 104 E 3 2 + 1 16 E 2 2 E 3 ,
    where the elementary symmetric functions E s are defined by (19.19.4). …
    19.36.2 1 - 3 14 E 2 + 1 6 E 3 + 9 88 E 2 2 - 3 22 E 4 - 9 52 E 2 E 3 + 3 26 E 5 - 1 16 E 2 3 + 3 40 E 3 2 + 3 20 E 2 E 4 + 45 272 E 2 2 E 3 - 9 68 ( E 3 E 4 + E 2 E 5 ) .
    19.36.4 z 1 = 2.10985 99098 8 , z 3 = 2.15673 49098 8 , Z 1 = 0.00977 77253 5 , z 2 = 2.12548 49098 8 , A = 2.13069 32432 1 , Z 2 = 0.00244 44313 4 , Z 3 = - Z 1 - Z 2 = - 0.01222 21566 9 , E 2 = -1.25480 14×10⁻⁴ , E 3 = -2.9212×10⁻⁷ .
    7: 4.1 Special Notation
    k , m , n integers.
    It is assumed the user is familiar with the definitions and properties of elementary functions of real arguments x . …
    8: 14.31 Other Applications
    §14.31(ii) Conical Functions
    These functions are also used in the Mehler–Fock integral transform (§14.20(vi)) for problems in potential and heat theory, and in elementary particle physics (Sneddon (1972, Chapter 7) and Braaksma and Meulenbeld (1967)). …
    9: 19.19 Taylor and Related Series
    Define the elementary symmetric function E s ( z ) by
    19.19.4 j = 1 n ( 1 + t z j ) = s = 0 n t s E s ( z ) ,
    19.19.5 T N ( 1 2 , z ) = ( - 1 ) M + N ( 1 2 ) M E 1 m 1 ( z ) E n m n ( z ) m 1 ! m n ! ,
    The number of terms in T N can be greatly reduced by using variables Z = 1 - ( z / A ) with A chosen to make E 1 ( Z ) = 0 . …
    E 1 ( Z ) = 0 , | Z j | < 1 .
    10: 19.10 Relations to Other Functions
    §19.10(ii) Elementary Functions