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The article discusses formulas for gamma function introduced by Scottish mathematician James Stirling, named Stirling's formula and Stirling's formula for the Gamma function. It mentions the approach in the first case which relies upon analysis of Wallis formula given by English mathematician John Wallis. It states that the approach that provides estimation to the factorial used in probability and statistical physics.

The article discusses the evaluation of the probability integral using the product formula for π of mathematician John Wallis. It explores the standard one-variable calculus method for evaluating the probability integral and functions using the approximation theory. It states that to approximate the integrand in the probability integral can yield a simpler evaluation of integrals. It proves that calculating the limits of the expression can be done using the Wallis product formula for π.

The article focuses on generalization of Wallis' formula of mathematician John Wallis using Glaisher-Kinkelin and Euler-Mascheroni constants.