Discovered by Ramanujan around 1910. From Hardy (1959, pp. 102-103),

(1) |

(2) |

(3) |

(4) |

In a more symmetric form, if , , , and for , 2, ..., 6, then

(5) |

The identity is a special case of Jackson's Identity.

**References**

Dixon, A. C. ``Summation of a Certain Series.'' *Proc. London Math. Soc.* **35**, 285-289, 1903.

Hardy, G. H. *Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed.* New York: Chelsea, 1959.

Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. *A=B.* Wellesley, MA: A. K. Peters, pp. 43, 126-127, and
183-184, 1996.

© 1996-9

1999-05-24