Search results
Results from the WOW.Com Content Network
Even if unavailable directly, the complete and incomplete beta function values can be calculated using functions commonly included in spreadsheet or computer algebra systems. In Microsoft Excel , for example, the complete beta function can be computed with the GammaLn function (or special.gammaln in Python's SciPy package):
For every odd positive integer +, the following equation holds: [3] (+) = ()!() +where is the n-th Euler Number.This yields: =,() =,() =,() =For the values of the Dirichlet beta function at even positive integers no elementary closed form is known, and no method has yet been found for determining the arithmetic nature of even beta values (similarly to the Riemann zeta function at odd integers ...
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.
where β is the Dirichlet beta function. Its numerical value [1] is approximately (sequence A006752 in the OEIS) G = 0.915 965 594 177 219 015 054 603 514 932 384 110 774 … Catalan's constant was named after Eugène Charles Catalan, who found quickly-converging series for its calculation and published a memoir on it in 1865. [2] [3]
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
The base e is the most economical choice of radix β > 1, [4] where the radix economy is measured as the product of the radix and the length of the string of symbols needed to express a given range of values. A binary number uses only two different digits, but it needs a lot of digits for representing a number; base 10 writes shorter numbers ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The Euler integral of the second kind is the gamma function [2] = For positive integers m and n , the two integrals can be expressed in terms of factorials and binomial coefficients : B ( n , m ) = ( n − 1 ) !