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elementary functions

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1: 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 .
2: 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 .
3: 4 Elementary Functions
Chapter 4 Elementary Functions
4: 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).
  • 5: 17.17 Physical Applications
    See Kassel (1995). …
    6: 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 . …
    7: 19.10 Relations to Other Functions
    §19.10(ii) Elementary Functions
    8: 4.44 Other Applications
    The Einstein functions and Planck’s radiation function are elementary combinations of exponentials, or exponentials and logarithms. …
    9: 4.46 Tables
    Extensive numerical tables of all the elementary functions for real values of their arguments appear in Abramowitz and Stegun (1964, Chapter 4). …
    10: Ranjan Roy