naginterfaces.library.specfun.jacellip_​real

naginterfaces.library.specfun.jacellip_real(u, m)[source]

jacellip_real evaluates the Jacobian elliptic functions sn, cn and dn.

For full information please refer to the NAG Library document for s21ca

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s21caf.html

Parameters
ufloat

The argument .

mfloat

The argument .

Returns
snfloat

The value of .

cnfloat

The value of .

dnfloat

The value of .

Raises
NagValueError
(errno )

On entry, is too large: it must be less than .

(errno )

On entry, is too large when used in conjunction with the supplied argument : it must be less than .

Notes

jacellip_real evaluates the Jacobian elliptic functions of argument and argument ,

where , called the amplitude of , is defined by the integral

The elliptic functions are sometimes written simply as , and , avoiding explicit reference to the argument .

Another nine elliptic functions may be computed via the formulae

(see Abramowitz and Stegun (1972)).

jacellip_real is based on a procedure given by Bulirsch (1960), and uses the process of the arithmetic-geometric mean ( in Abramowitz and Stegun (1972)). Constraints are placed on the values of and in order to avoid the possibility of machine overflow.

References

Abramowitz, M and Stegun, I A, 1972, Handbook of Mathematical Functions, (3rd Edition), Dover Publications

Bulirsch, R, 1960, Numerical calculation of elliptic integrals and elliptic functions, Numer. Math. (7), 76–90