This function evaluates the first derivative of the Weierstrass' ℘ function in the equianharmonic case for complex argument with unit period parallelogram.
Function Return Value
CWPQD — Complex function value. (Output)
Required Arguments
Z — Complex argument for which the function value is desired. (Input)
FORTRAN 90 Interface
Generic: CWPQD (Z)
Specific: The specific interface names are C_CWPQD and Z_CWPQD.
FORTRAN 77 Interface
Complex: CWPQD (Z)
Double complex: The double complex name is ZWPQD.
Description
The Weierstrass' ℘ function, ℘(z) = ℘(z | ω, ωʹ), is an elliptic function of order two with periods 2ω and 2 ωʹ and a double pole at z = 0. CWPQD(Z) computes the derivative of ℘(z | ω, ωʹ) with
CWPQ computes ℘(z | ω, ωʹ).
The input argument is first reduced to the fundamental parallelogram of all z satisfying
Then, a rational approximation is used.
All arguments are valid with the exception of the lattice points
which are the poles of CWPQ. If the argument is a lattice point, then b = AMACH(2), the largest floating-point number, is returned.
Function CWPQD is based on code by Eckhardt (1980). Also, see Eckhardt (1977).
Example
In this example, ℘(0.25 + 0.14437567i) is computed and printed.
USE CWPQD_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
COMPLEX VALUE, Z
! Compute
Z = (0.25, 0.14437567)
VALUE = CWPQD(Z)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) Z, VALUE
99999 FORMAT (' CWPQD(', F6.3, ',', F6.3, ') = (', &
F6.3, ',', F6.3, ')')
END
Output
CWPQD( 0.250, 0.144) = ( 0.028,85.934)
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