jacobi_theta_functions: Jacobi Theta Functions

In boostmath: 'R' Bindings for the 'Boost' Math Functions

Jacobi Theta Functions

Description

Functions to compute the Jacobi theta functions (\theta_1, \theta_2, \theta_3, \theta_4) parameterised by either (q) or (\tau).

Usage

jacobi_theta1(x, q)

jacobi_theta1tau(x, tau)

jacobi_theta2(x, q)

jacobi_theta2tau(x, tau)

jacobi_theta3(x, q)

jacobi_theta3tau(x, tau)

jacobi_theta3m1(x, q)

jacobi_theta3m1tau(x, tau)

jacobi_theta4(x, q)

jacobi_theta4tau(x, tau)

jacobi_theta4m1(x, q)

jacobi_theta4m1tau(x, tau)

Arguments

x	Input value
q	The nome parameter of the Jacobi theta function (0 < q < 1)
tau	The nome parameter of the Jacobi theta function (tau = u + iv, where u and v are real numbers)

Value

A single numeric value with the computed Jacobi theta function.

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Jacobi Theta Functions
x <- 0.5
q <- 0.9
tau <- 1.5
jacobi_theta1(x, q)
jacobi_theta1tau(x, tau)
jacobi_theta2(x, q)
jacobi_theta2tau(x, tau)
jacobi_theta3(x, q)
jacobi_theta3tau(x, tau)
jacobi_theta3m1(x, q)
jacobi_theta3m1tau(x, tau)
jacobi_theta4(x, q)
jacobi_theta4tau(x, tau)
jacobi_theta4m1(x, q)
jacobi_theta4m1tau(x, tau)

boostmath documentation built on Dec. 15, 2025, 5:07 p.m.