Search Results for ""

A divergent sequence is a sequence that is not convergent.

A series which is not convergent. Series may diverge by marching off to infinity or by oscillating. Divergent series have some curious properties. For example, rearranging ...

The great success mathematicians had studying hypergeometric functions _pF_q(a_1,...,a_p;b_1,...,b_q;z) for the convergent cases (p<=q+1) prompted attempts to provide ...

A series is said to be convergent if it approaches some limit (D'Angelo and West 2000, p. 259). Formally, the infinite series sum_(n=1)^(infty)a_n is convergent if the ...

The series sumf(n) for a monotonic nonincreasing f(x) is convergent if lim_(x->infty)^_(e^xf(e^x))/(f(x))<1 and divergent if lim_(x->infty)__(e^xf(e^x))/(f(x))>1.

Wynn's epsilon-method is a method for numerical evaluation of sums and products that samples a number of additional terms in the series and then tries to extrapolate them by ...

A sequence produced by the instructions "reverse, add to the original, then sort the digits." For example, after 668, the next iteration is given by 668+866=1534, so the next ...

Let Gamma(z) be the gamma function and n!! denote a double factorial, then [(Gamma(m+1/2))/(Gamma(m))]^2[1/m+(1/2)^21/(m+1)+((1·3)/(2·4))^21/(m+2)+...]_()_(n) ...

An fairly good numerical integration technique. The method is also available in the Wolfram Language using the option Method -> DoubleExponential to NIntegrate.

Infinite series of various simple functions of the logarithm include sum_(k=1)^^^inftylnk = 1/2ln(2pi) (1) sum_(k=1)^^^infty(-1)^klnk = 1/2ln(1/2pi) (2) ...