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In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
The binomial coefficients can be arranged to form Pascal's triangle, in which each entry is the sum of the two immediately above. Visualisation of binomial expansion up to the 4th power. In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem.
In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series expansion of functions, and with the Euler–MacLaurin formula. These polynomials occur in the study of many special functions and, in particular, the Riemann zeta function and the Hurwitz ...
Download as PDF; Printable version; ... Binomial; Taylor; ... the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in ...
Binomial expansion. Add languages. Add links. Article; Talk; ... Download QR code; Print/export Download as PDF; Printable version; In other projects
The usual argument to compute the sum of the binomial series goes as follows. Differentiating term-wise the binomial series within the disk of convergence | x | < 1 and using formula , one has that the sum of the series is an analytic function solving the ordinary differential equation (1 + x)u′(x) − αu(x) = 0 with initial condition u(0) = 1.
Download as PDF; Printable version; In other projects Wikidata item; ... is the binomial coefficient and () is the falling factorial. Newtonian series ...
Download QR code; Print/export Download as PDF; Printable version; In other projects ... is a mathematical identity involving sums of binomial coefficients. It states ...