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alpha_n(z) = int_1^inftyt^ne^(-zt)dt (1) = n!z^(-(n+1))e^(-z)sum_(k=0)^(n)(z^k)/(k!). (2) It is equivalent to alpha_n(z)=E_(-n)(z), (3) where E_n(z) is the En-function.

A map F from R^n to R^n is area-preserving if m(F^(-1)(A))=m(A) for every subregion A of R^n, where m(A) is the n-dimensional measure of A. A linear transformation is ...

For a simple continued fraction x=[a_0,a_1,...] with convergents p_n/q_n, the fundamental recurrence relation is given by p_nq_(n-1)-p_(n-1)q_n=(-1)^(n+1).

A delta sequence is a sequence of strongly peaked functions for which lim_(n->infty)int_(-infty)^inftydelta_n(x)f(x)dx=f(0) (1) so that in the limit as n->infty, the ...

The equations are x = ((lambda-lambda_0)(1+costheta))/(sqrt(2+pi)) (1) y = (2theta)/(sqrt(2+pi)), (2) where theta is the solution to theta+sintheta=(1+1/2pi)sinphi. (3) This ...

A sequence of n 0s and 1s is called an odd sequence if each of the n sums sum_(i=1)^(n-k)a_ia_(i+k) for k=0, 1, ..., n-1 is odd.

F(x,s) = sum_(m=1)^(infty)(e^(2piimx))/(m^s) (1) = psi_s(e^(2piix)), (2) where psi_s(x) is the polygamma function.

Let D be a subset of the nonnegative integers Z^* with the properties that (1) the integer 0 is in D and (2) any time that n is in D, one can show that n+1 is also in D. ...

A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = 1/3u^3-1/2v^2. (3) The coefficients of the coefficients of the first fundamental form are E ...

Let X and Y be topological spaces. Then their join is the factor space X*Y=(X×Y×I)/∼, (1) where ∼ is the equivalence relation (x,y,t)∼(x^',y^',t^')<=>{t=t^'=0 and x=x^'; or ; ...