About the Project
NIST

logarithm function

AdvancedHelp

(0.006 seconds)

1—10 of 391 matching pages

1: 4.11 Sums
§4.11 Sums
2: 4.2 Definitions
§4.2(i) The Logarithm
The general logarithm function Ln z is defined by …
§4.2(ii) Logarithms to a General Base a
Natural logarithms have as base the unique positive number …
3: 4.47 Approximations
§4.47 Approximations
§4.47(i) Chebyshev-Series Expansions
4: 4.46 Tables
§4.46 Tables
5: 5.10 Continued Fractions
§5.10 Continued Fractions
5.10.1 Ln Γ ( z ) + z - ( z - 1 2 ) ln z - 1 2 ln ( 2 π ) = a 0 z + a 1 z + a 2 z + a 3 z + a 4 z + a 5 z + ,
6: 4.1 Special Notation
k , m , n integers.
The main purpose of the present chapter is to extend these definitions and properties to complex arguments z . The main functions treated in this chapter are the logarithm ln z , Ln z ; the exponential exp z , e z ; the circular trigonometric (or just trigonometric) functions sin z , cos z , tan z , csc z , sec z , cot z ; the inverse trigonometric functions arcsin z , Arcsin z , etc. …
7: 4.10 Integrals
§4.10(i) Logarithms
4.10.1 d z z = ln z ,
4.10.2 ln z d z = z ln z - z ,
4.10.4 d z z ln z = ln ( ln z ) ,
4.10.7 0 x d t ln t = li ( x ) , x > 1 .
8: 4.8 Identities
§4.8(i) Logarithms
4.8.1 Ln ( z 1 z 2 ) = Ln z 1 + Ln z 2 .
4.8.3 Ln z 1 z 2 = Ln z 1 - Ln z 2 ,
4.8.10 exp ( ln z ) = exp ( Ln z ) = z .
4.8.13 ln ( a x ) = x ln a , a > 0 .
9: 4.3 Graphics
See accompanying text
Figure 4.3.1: ln x and e x . … Magnify
§4.3(ii) Complex Arguments: Conformal Maps
See accompanying text
Figure 4.3.3: ln ( x + i y ) (principal value). … Magnify 3D Help
10: 5.3 Graphics
See accompanying text
Figure 5.3.2: ln Γ ( x ) . … Magnify