TOPICS
Search

Search Results for ""


1 - 10 of 168 for SummationSearch Results
The analytic summation of a hypergeometric series. Powerful general techniques of hypergeometric summation include Gosper's algorithm, Sister Celine's method, Wilf-Zeilberger ...
Einstein summation is a notational convention for simplifying expressions including summations of vectors, matrices, and general tensors. There are essentially three rules of ...
Summation by parts for discrete variables is the equivalent of integration by parts for continuous variables Delta^(-1)[v(x)Deltau(x)]=u(x)v(x)-Delta^(-1)[Eu(x)Deltav(x)], ...
The indefinite summation operator Delta^(-1) for discrete variables, is the equivalent of integration for continuous variables. If DeltaY(x)=y(x), then Delta^(-1)y(x)=Y(x).
An algorithm for finding closed form hypergeometric identities. The algorithm treats sums whose successive terms have ratios which are rational functions. Not only does it ...
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 ...
where _2F_1(a,b;c;z) is a hypergeometric function and _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function.
sum_(k=-n)^n(-1)^k(n+b; n+k)(n+c; c+k)(b+c; b+k)=(Gamma(b+c+n+1))/(n!Gamma(b+1)Gamma(c+1)), where (n; k) is a binomial coefficient and Gamma(x) is a gamma function.
A solution of a linear homogeneous ordinary differential equation with polynomial coefficients.
Given a hypergeometric series sum_(k)c_k, c_k is called a hypergeometric term (Koepf 1998, p. 12).
1|2|3|4 ... 17 Next

...