The continued fraction expansion of Gauss' hypergeometric function and a new application to the tangent function

ABSTRACT

Starting from a formula for tan(nx) in the celebrated Hakmem report [1] we find a continued fraction expansion for tan(nx) in terms of tan(x).

Notes

¹Some information found on the web: A legendary collection of neat mathematical and programming hacks contributed by many people at MIT and elsewhere. (The title “HAKMEM” is a 6-letterism for “hacks memo”.) It is notable as an early compendium of algorithmic techniques. One of the major contributors is Bill Gosper, known for Gosper's algorithm (telescopic summation). Because his mathematics is largely self-taught and a number of his original formulæ have inspired professional mathematicians to write papers developing them into fully fledged theories, he has been considered a modern day Ramanujan.

Additional information

Notes on contributors

Helmut Prodinger

Helmut Prodinger was supported by an incentive grant of the NRF of South Africa. August 9, 2036