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The earliest q-analog studied in detail is the basic hypergeometric series, which was introduced in the 19th century. [1] q-analogs are most frequently studied in the mathematical fields of combinatorics and special functions. In these settings, the limit q → 1 is often formal, as q is often discrete-valued (for example, it may represent a ...
In mathematics, basic hypergeometric series, or q-hypergeometric series, are q-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series. A series x n is called hypergeometric if the ratio of successive terms x n+1 /x n is a rational function of n.
The logarithm of the Euler function is the sum of the logarithms in the product expression, each of which may be expanded about q = 0, yielding (()) = =, which is a Lambert series with coefficients -1/n. The logarithm of the Euler function may therefore be expressed as
This is a list of q-analogs in mathematics and related fields. Algebra ... q-Jacobi polynomials: ... Basic hypergeometric series;
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
Yellowstone just aired its series finale on Dec. 15 after five seasons. Grimes also spoke to Men's Health about the Paramount Network series and his onscreen father Kevin Costner's early exit from it.
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