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A quantity defined for a conic section which can be given in terms of semimajor a and semiminor axes b. interval curve e e=0 circle 0 0<e<1 ellipse sqrt(1-(b^2)/(a^2)) e=1 ...

The second-order ordinary differential equation y^('')+[(alphaeta)/(1+eta)+(betaeta)/((1+eta)^2)+gamma]y=0, where eta=e^(deltax).

The elliptic exponential function eexp_(a,b)(u) gives the value of x in the elliptic logarithm eln_(a,b)(x)=1/2int_infty^x(dt)/(sqrt(t^3+at^2+bt)) for a and b real such that ...

A number D that possesses no common divisor with a prime number p is either a quadratic residue or nonresidue of p, depending whether D^((p-1)/2) is congruent mod p to +/-1.

A sequence {a_1,a_2,a_3,...} fulfils a given property eventually if it fulfils it from some point onward, or, more precisely, if the property is fulfilled by the subsequence ...

An efficient version of the Walsh transform that requires O(nlnn) operations instead of the n^2 required for a direct Walsh transform (Wolfram 2002, p. 1072).

There are seven frieze groups, which can be written in orbifold notation as *22infty, 2*infty, 22infty, *inftyinfty, infty*, inftyx, inftyinfty.

The series sum_(k=1)^inftykr^k=sum_(k=1)^inftysum_(i=k)^inftyr^i=r/((1-r)^2), valid for 0<r<1.

The partial differential equation w_t-6(w+epsilon^2w^2)w_x+w_(xxx)=0, which can also be rewritten (w)_t+(-3w^2-2epsilon^2w^3+w_(xx))_x=0.

A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the ...