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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.
PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series, algebraic numbers, and transcendental functions. [3]
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
If p < q + 1 then the ratio of coefficients tends to zero. This implies that the series converges for any finite value of z and thus defines an entire function of z. An example is the power series for the exponential function. If p = q + 1 then the ratio of coefficients tends to one.
A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
Formula weight calculator: The input is a chemical molecular formula, using the periodic-table symbols and notation, and there is a button to work out the percentages of its constituents. Astronomical calculator: The input is a date and one or multiple celestial bodies (usually the sun, moon, planets, planetoids or comets). The program ...
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The q-Pochhammer symbol is closely related to the enumerative combinatorics of partitions.The coefficient of in (;) = = is the number of partitions of m into at most n parts.