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Pathological functions that are continuous but differentiable only on a set of points of measure zero are sometimes known as monsters of real analysis. Examples include the ...

The integral phi(t,u)=int(e^(piitx^2+2piiux))/(e^(2piix)-1)dx which is related to the Jacobi theta functions, mock theta functions, Riemann zeta function, and Siegel theta ...

In above figure, which constitutes a modified version of the painting Tirets by Francois Morellet, small circles seem to appear and disappear as the eye is moved over them.

sum_(k=0)^(infty)[((m)_k)/(k!)]^3 = 1+(m/1)^3+[(m(m+1))/(1·2)]^3+... (1) = (Gamma(1-3/2m))/([Gamma(1-1/2m)]^3)cos(1/2mpi), (2) where (m)_k is a Pochhammer symbol and Gamma(z) ...

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

A knot K embedded in R^3=C_z×R_t, where the three-dimensional space R^3 is represented as a direct product of a complex line C with coordinate z and a real line R with ...

A nonempty finite set of n×n integer matrices for which there exists some product of the matrices in the set which is equal to the zero matrix.

For a given n, is the problem of determining if a set is mortal solvable? n=1 is solvable, n=2 is unknown, and n>=3 is unsolvable.

Let B dollars be borrowed at an interest rate of i per month, where i is the annual rate divided by 12, and assume the mortgage needs to be paid back in n months. Then the ...

An oval whose construction is illustrated in the above diagram.