Jackson's Identity

The q-hypergeometric function identity

 _rphi_s^'[a,qsqrt(a),-qsqrt(a),1/b,1/c,1/d,1/e,1/f; sqrt(a),-sqrt(a),abq,acq,adq,aeq,afq] 



_rphi_s^' is a q-hypergeometric function, and one of b, c, d, e, or f is equal to q^m (Hardy 1999, pp. 108-109). This identity includes the Dougall-Ramanujan identity as a special case.

See also

Dougall-Ramanujan Identity, Jackson-Slater Identity, q-Hypergeometric Function

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Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 66-72, 1935.Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 109-110, 1999.Jackson, F. H. "Summation of q-Hypergeometric Series." Messenger Math. 50, 101-112, 1921.

Referenced on Wolfram|Alpha

Jackson's Identity

Cite this as:

Weisstein, Eric W. "Jackson's Identity." From MathWorld--A Wolfram Web Resource.

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