Description Usage Arguments Details Value See Also Examples

Approximation of "the" Jacobi theta function using the first `nn`

factors in its triple product version

1 | ```
jacobiTheta(z, tau, nn = 30L)
``` |

`z` |
Complex number; the point in the complex plane to which the output of the function is mapped |

`tau` |
Complex number; the so-called half-period ratio, must have a positive imaginary part |

`nn` |
Integer; number of factors to be used when approximating the triple product (default = 30) |

This function approximates the Jacobi theta function theta(z; tau) which is the sum of exp(pi*i*n^2*tau + 2*pi*i*n*z) for n in -Inf, Inf. It uses, however, the function's triple product representation. See https://en.wikipedia.org/wiki/Theta_function for details. This function has been implemented in C++, but it is only slightly faster than well-crafted R versions, because the calculation can be nicely vectorized in R.

The value of the function for `z`

and `tau`

.

Other maths:
`blaschkeProd()`

,
`juliaNormal()`

,
`mandelbrot()`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
phasePortrait(jacobiTheta, moreArgs = list(tau = 1i/2-1/4),
pType = "p", xlim = c(-2, 2), ylim = c(-2, 2),
nCores = 1) # Max. two cores on CRAN, not a limit for your use
phasePortrait(jacobiTheta, moreArgs = list(tau = 1i/2-1/2),
pType = "p", xlim = c(-2, 2), ylim = c(-2, 2),
nCores = 1)
phasePortrait(jacobiTheta, moreArgs = list(tau = 1i/3+1/3),
pType = "p", xlim = c(-2, 2), ylim = c(-2, 2),
nCores = 1)
phasePortrait(jacobiTheta, moreArgs = list(tau = 1i/4+1/2),
pType = "p", xlim = c(-2, 2), ylim = c(-2, 2),
nCores = 1)
``` |

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