Tanh-sinh quadrature

Tanh-Sinh quadrature is a method for numerical integration introduced by Hidetosi Takahasi and Masatake Mori in 1974. It uses hyperbolic functions in the change of variables Tanh-Sinh quadrature is a method for numerical integration introduced by Hidetosi Takahasi and Masatake Mori in 1974. It uses hyperbolic functions in the change of variables to transform an integral on the interval x ∈ (−1, +1) to an integral on the entire real line t ∈ (−∞,+∞), the two integrals having the same value. After this transformation, the integrand decays with a double exponential rate, and thus, this method is also known as the Double Exponential (DE) formula. For a given step size h, the integral is approximated by the sum with the abscissas