  The beta integral is applied to accelerate the hypergeometric function $2 F
1\left\{1, B; C ; w\right\}$ to derive new infinite series for constants such
as $\pi$ and values of the gamma function. A compendium of new infinite series
is given. Ramanujan-like formulas for pi are also derived based on elementary
inverse trigonometric functions, including a formula with rational values that
adds 2.5 digits per terms, which makes the series much more compact than
similar formulas in the existing literature.
