This is a collection of formulas discovered by the Indian Mathematician Srinivasa Ramanujan (1887-1920) that appears in the book “A Passion for Mathematics” by Clifford A Pickover.

Here, the infinite product symbolized by , steps through every prime number.

Note that the term in parentheses can be reduced to , where is the golden ratio.

Where is the Euler-Mascheroni constant.

The following formulas used Pochhammer notation. In particular,

The subscript value effectively tells you how many terms to include in the product.

You can download a pdf version from here.