| 释义 |
Natural LogarithmThe Logarithm having base e, where
 | (1) |
 | (2) |
 . The natural logarithm can also be defined for Complex Numbers as
 | (3) |
 is the Modulus and  is the Argument. The natural logarithm is especially useful in Calculus because its Derivativeis given by the simple equation
 | (4) |
 | (5) |
The Mercator Series
 | (6) |
Continued Fraction representations of logarithmic functions include
 | (7) |
 | (8) |
For a Complex Number  , the natural logarithm satisfies
 | (9) |
 | (10) |
 is the Principal Value.
Some special values of the natural logarithm are
 | (11) |
 | (12) |
 | (13) |
 | (14) |
An identity for the natural logarithm of 2 discovered using the PSLQ Algorithm is
 | (15) |
 is given by the periodic sequence obtained by appending copies of  (in other words, for  ) (Bailey et al. 1995, Bailey and Plouffe).See also e, Jensen's Formula, Lg, Logarithm
References
Bailey, D.; Borwein, P.; and Plouffe, S. ``On the Rapid Computation of Various Polylogarithmic Constants.'' http://www.cecm.sfu.ca/~pborwein/PAPERS/P123.ps.Bailey, D. and Plouffe, S. ``Recognizing Numerical Constants.'' http://www.cecm.sfu.ca/organics/papers/bailey/. |