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This function estimates the integral using the Gaussian-Legendre quadrature method. It uses Legendre polynomial roots and weights to compute the integral over the given interval.

Usage

gaussian_legendre_integral(
  period = c(0, 1),
  y_tilde,
  v_tilde,
  tau_tilde,
  n_points = 10
)

Arguments

period

Numeric vector, the integration interval, default is `c(0, 1)`.

y_tilde

Numeric, parameter for the exponential function in the integrand.

v_tilde

Numeric, parameter for the exponential function in the integrand.

tau_tilde

Numeric, parameter for the exponential function in the integrand.

n_points

Integer, the number of Gaussian points to use for the integration.

Value

A list containing: - `integral_estimate`: Estimated integral using the Gaussian-Legendre quadrature. - `time_avg`: Time taken to perform the calculation.