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The question of whether a solution to a given problem exists. The existence problem can be solved in the affirmative without actually finding a solution to the original ...

The sum of the absolute squares of the spherical harmonics Y_l^m(theta,phi) over all values of m is sum_(m=-l)^l|Y_l^m(theta,phi)|^2=(2l+1)/(4pi). (1) The double sum over m ...

A problem in the theory of algebraic invariants that was solved by Hilbert using an existence proof.

A Sheffer sequence for (1,f(t)) is called the associated sequence for f(t), and a sequence s_n(x) of polynomials satisfying the orthogonality conditions ...

The Fourier transform of the Heaviside step function H(x) is given by F_x[H(x)](k) = int_(-infty)^inftye^(-2piikx)H(x)dx (1) = 1/2[delta(k)-i/(pik)], (2) where delta(k) is ...

For s_1,s_2=+/-1, lim_(epsilon_1->0; epsilon_2->0)1/(x_1-is_1epsilon_1)1/(x_2-is_2epsilon_2) =[PV(1/(x_1))+ipis_1delta(x_1)][PV(1/(x_2))+ipis_2delta(x_2)] ...

"Neighborhood" is a word with many different levels of meaning in mathematics. One of the most general concepts of a neighborhood of a point x in R^n (also called an ...

The permutation symbol (Evett 1966; Goldstein 1980, p. 172; Aris 1989, p. 16) is a three-index object sometimes called the Levi-Civita symbol (Weinberg 1972, p. 38; Misner et ...

The Fourier transform of the constant function f(x)=1 is given by F_x[1](k) = int_(-infty)^inftye^(-2piikx)dx (1) = delta(k), (2) according to the definition of the delta ...

Modus tollens is a valid argument form in propositional calculus in which p and q are propositions. If p implies q, and q is false, then p is false. Also known as an indirect ...