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q-theta function

From Wikipedia, the free encyclopedia

In mathematics, the q-theta function (or modified Jacobi theta function) is a type of q-series which is used to define elliptic hypergeometric series. [1][2] It is given by

where one takes 0 ≤ |q| < 1. It obeys the identities

It may also be expressed as:

where is the q-Pochhammer symbol.

See also

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References

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  1. ^ Gasper, George; Rahman, Mizan (2004). Basic Hypergeometric Series. doi:10.1017/CBO9780511526251. ISBN 9780521833578.
  2. ^ Spiridonov, V. P. (2008). "Essays on the theory of elliptic hypergeometric functions". Russian Mathematical Surveys. 63 (3): 405–472. arXiv:0805.3135. Bibcode:2008RuMaS..63..405S. doi:10.1070/RM2008v063n03ABEH004533. S2CID 16996893.