A Series involving coefficients of the form

(1) | |||

(2) |

(Andrews 1986). The symbols

(3) | |||

(4) |

are sometimes also used when discussing -series.

There are a great many beautiful identities involving -series, some of which follow directly by taking the
*q*-Analog of standard combinatorial identities, e.g., the *q*-Binomial Theorem

(5) |

(6) |

(7) |

**References**

Andrews, G. E.
*-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra.*
Providence, RI: Amer. Math. Soc., 1986.

Berndt, B. C. ``-Series.'' Ch. 27 in *Ramanujan's Notebooks, Part IV.* New York: Springer-Verlag, pp. 261-286, 1994.

Gasper, G. and Rahman, M. *Basic Hypergeometric Series.* Cambridge, England: Cambridge University Press, 1990.

Gosper, R. W. ``Experiments and Discoveries in -Trigonometry.'' Unpublished manuscript.

© 1996-9

1999-05-25