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Jacobi Elliptic Functions

Source: R/jacobi_elliptic_functions.R
jacobi_elliptic_functions.Rd

Functions to compute the Jacobi elliptic functions: sn, cn, dn, and others.

Usage

jacobi_elliptic(k, u)

jacobi_cd(k, u)

jacobi_cn(k, u)

jacobi_cs(k, u)

jacobi_dc(k, u)

jacobi_dn(k, u)

jacobi_ds(k, u)

jacobi_nc(k, u)

jacobi_nd(k, u)

jacobi_ns(k, u)

jacobi_sc(k, u)

jacobi_sd(k, u)

jacobi_sn(k, u)

Arguments

k

Elliptic modulus (0 <= k < 1)

u

Argument of the elliptic functions

Value

For jacobi_elliptic, a list containing the values of the Jacobi elliptic functions: sn, cn, dn. For individual functions, a single numeric value is returned.

See also

Boost Documentation for more details on the mathematical background.

Examples

# Jacobi Elliptic Functions
k <- 0.5
u <- 2
jacobi_elliptic(k, u)
#> $sn
#> [1] 0.9628982
#> 
#> $cn
#> [1] -0.269865
#> 
#> $dn
#> [1] 0.8764741
#> 
# Individual Jacobi Elliptic Functions
jacobi_cd(k, u)
#> [1] -0.3078984
jacobi_cn(k, u)
#> [1] -0.269865
jacobi_cs(k, u)
#> [1] -0.2802632
jacobi_dc(k, u)
#> [1] -3.247825
jacobi_dn(k, u)
#> [1] 0.8764741
jacobi_ds(k, u)
#> [1] 0.9102458
jacobi_nc(k, u)
#> [1] -3.705557
jacobi_nd(k, u)
#> [1] 1.140935
jacobi_ns(k, u)
#> [1] 1.038531
jacobi_sc(k, u)
#> [1] -3.568074
jacobi_sd(k, u)
#> [1] 1.098604
jacobi_sn(k, u)
#> [1] 0.9628982