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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.
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 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 ...
The q-Pochhammer symbol is the subject of a number of q-series identities, ... Encyclopedia of Mathematics and Its Applications, 96, Cambridge ... Toggle the table of ...
Toggle the table of contents. Q series. Add languages. ... Q series may refer to: ... Pentax Q series, cameras; Mathematics. Q-series; Hypergeometric q-series; See also.
q-Bessel polynomials; q-Charlier polynomials; q-Hahn polynomials; q-Jacobi polynomials: Big q-Jacobi polynomials; Continuous q-Jacobi polynomials; Little q-Jacobi polynomials; q-Krawtchouk polynomials; q-Laguerre polynomials; q-Meixner polynomials; q-Meixner–Pollaczek polynomials; q-Racah polynomials
In 1981, Richard Dean showed the quaternion group can be realized as the Galois group Gal(T/Q) where Q is the field of rational numbers and T is the splitting field of the polynomial x 8 − 72 x 6 + 180 x 4 − 144 x 2 + 36 {\displaystyle x^{8}-72x^{6}+180x^{4}-144x^{2}+36} .
Table of Clebsch-Gordan coefficients; Table of derivatives; Table of divisors; Table of integrals; Table of mathematical symbols; Table of prime factors; Taylor series; Timeline of mathematics; Trigonometric identities; Truth table