About the Project

complex variable

AdvancedHelp

(0.011 seconds)

1—10 of 504 matching pages

1: 32.12 Asymptotic Approximations for Complex Variables
§32.12 Asymptotic Approximations for Complex Variables
2: 5.1 Special Notation
j , m , n nonnegative integers.
z = x + i y complex variable.
a , b , q , s , w real or complex variables with | q | < 1 .
3: 32.1 Special Notation
m , n integers.
z complex variable.
4: 21.8 Abelian Functions
An Abelian function is a 2 g -fold periodic, meromorphic function of g complex variables. In consequence, Abelian functions are generalizations of elliptic functions (§23.2(iii)) to more than one complex variable. …
5: 4.34 Derivatives and Differential Equations
4.34.7 d 2 w d z 2 a 2 w = 0 ,
4.34.8 ( d w d z ) 2 a 2 w 2 = 1 ,
4.34.12 w = ( 1 / a ) sinh ( a z + c ) ,
4.34.13 w = ( 1 / a ) cosh ( a z + c ) ,
4.34.14 w = ( 1 / a ) coth ( a z + c ) ,
6: 4.20 Derivatives and Differential Equations
4.20.9 d 2 w d z 2 + a 2 w = 0 ,
4.20.10 ( d w d z ) 2 + a 2 w 2 = 1 ,
4.20.12 w = A cos ( a z ) + B sin ( a z ) ,
4.20.13 w = ( 1 / a ) sin ( a z + c ) ,
4.20.14 w = ( 1 / a ) tan ( a z + c ) ,
7: 6.1 Special Notation
x real variable.
z complex variable.
8: 25.1 Special Notation
k , m , n nonnegative integers.
s = σ + i t complex variable.
z = x + i y complex variable.
9: 4.14 Definitions and Periodicity
4.14.4 tan z = sin z cos z ,
4.14.5 csc z = 1 sin z ,
4.14.6 sec z = 1 cos z ,
4.14.8 sin ( z + 2 k π ) = sin z ,
4.14.9 cos ( z + 2 k π ) = cos z ,
10: 4.28 Definitions and Periodicity
4.28.2 cosh z = e z + e z 2 ,
4.28.3 cosh z ± sinh z = e ± z ,
4.28.5 csch z = 1 sinh z ,
4.28.9 cos ( i z ) = cosh z ,
4.28.12 sec ( i z ) = sech z ,