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The series with sum sum_(n=0)^infty1/(F_(2^n))=1/2(7-sqrt(5)), where F_k is a Fibonacci number (Honsberger 1985).

If {f_n} is a sequence of measurable functions, with 0<=f_n<=f_(n+1) for every n, then intlim_(n->infty)f_ndmu=lim_(n->infty)intf_ndmu.

The second-order ordinary differential equation y^('')+[alpha/(cosh^2(ax))+betatanh(ax)+gamma]y=0.

n events are said to be mutually exclusive if the occurrence of any one of them precludes any of the others. Therefore, for events X_1, ..., X_n, the conditional probability ...

A curve also known as swan-like curve or streamline. It is given by the polar equation r=atheta+b, where a>0.

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

A quantity that is nonzero everywhere is said to be nonvanishing. For instance, the values of x^2+1 are nonvanishing for real x, while those of x^2 are not (since x^2 ...

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.

Let alpha and beta be any ordinal numbers, then ordinal exponentiation is defined so that if beta=0 then alpha^beta=1. If beta is not a limit ordinal, then choose gamma such ...

Two representations of a group chi_i and chi_j are said to be orthogonal if sum_(R)chi_i(R)chi_j(R)=0 for i!=j, where the sum is over all elements R of the representation.