Ads
related to: q-series math examples problems 5th grade multiplication
Search results
Results From The WOW.Com Content Network
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.
For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. [2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9.
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} .
Since the multiplication is non-commutative, the quotient quantities p q −1 or q −1 p are different (except if p and q are scalar multiples of each other or if one is a scalar): the notation p / q is ambiguous and should not be used.
Multiplication lies outside of AC 0 [p] for any prime p, meaning there is no family of constant-depth, polynomial (or even subexponential) size circuits using AND, OR, NOT, and MOD p gates that can compute a product. This follows from a constant-depth reduction of MOD q to multiplication. [26]
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 ...