“q-Series”的概念、定义、习题解题方法及翻译-数学辞典

单词

q-Series

释义

q-Series

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 theq-Analog of standard combinatorial identities, e.g., the q-Binomial Theorem

(5)

(

; Andrews 1986, p. 10) and q-Vandermonde Sum

(6)

where

is a Heine Hypergeometric Series. Other

-series identities, e.g., the Jacobi Identities,Rogers-Ramanujan Identities, and Heine Hypergeometric Series identity

(7)

seem to arise out of the blue.

See also Borwein Conjectures, Fine's Equation, Gaussian Coefficient, Heine Hypergeometric Series,Jackson's Identity, Jacobi Identities, Mock Theta Function, q-Analog,q-Binomial Theorem,q-Cosine, q-Factorial, Q-Function,q-Gamma Function, q-Sine, Ramanujan Psi Sum,Ramanujan Theta Functions, Rogers-Ramanujan Identities

References

q-Series

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 Unpublished manuscript.

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