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Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then the Selberg zeta function is defined as ...

A sequence is an ordered set of mathematical objects. Sequences of object are most commonly denoted using braces. For example, the symbol {2n}_(n=1)^infty denotes the ...

A generalization of the Bessel differential equation for functions of order 0, given by zy^('')+y^'+(z+A)y=0. Solutions are y=e^(+/-iz)_1F_1(1/2∓1/2iA;1;∓2iz), where ...

Interest which is paid only on the principal and not on the additional amount generated by previous interest payments. A formula for computing simple interest is ...

A smooth map f:S^1->R^3 whose image has singularities. In particular, in the theory of Vassiliev's knot invariants, singular knots with a finite number of ordinary double ...

The m+1 ellipsoidal harmonics when kappa_1, kappa_2, and kappa_3 are given can be arranged in such a way that the rth function has r-1 zeros between -a^2 and -b^2 and the ...

A map which uses a set of rules to transform elements of a sequence into a new sequence using a set of rules which "translate" from the original sequence to its ...

Any linear combination of real spherical harmonics A_lP_l(costheta)+sum_(m=1)^l[A_l^mcos(mphi)+B_l^msin(mphi)]P_l^m(costheta) for l fixed whose sum is not premultiplied by a ...

The "temperature" of a curve Gamma is defined as T=1/(ln((2l)/(2l-h))), where l is the length of Gamma and h is the length of the perimeter of the convex hull. The ...

A number of attractive 8-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...