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Using the notation of Byerly (1959, pp. 252-253), Laplace's equation can be reduced to (1) where alpha = cint_c^lambda(dlambda)/(sqrt((lambda^2-b^2)(lambda^2-c^2))) (2) = ...

In spherical coordinates, the scale factors are h_r=1, h_theta=rsinphi, h_phi=r, and the separation functions are f_1(r)=r^2, f_2(theta)=1, f_3(phi)=sinphi, giving a Stäckel ...

A lattice-ordered set is a poset (L,<=) in which each two-element subset {a,b} has an infimum, denoted inf{a,b}, and a supremum, denoted sup{a,b}. There is a natural ...

An algebra <L; ^ , v > is called a lattice if L is a nonempty set, ^ and v are binary operations on L, both ^ and v are idempotent, commutative, and associative, and they ...

The lattice method is an alternative to long multiplication for numbers. In this approach, a lattice is first constructed, sized to fit the numbers being multiplied. If we ...

A polygon whose vertices are points of a point lattice. Regular lattice n-gons exists only for n=3, 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963, Maehara 1993). A ...

Cubic lattice sums include the following: b_2(2s) = sum^'_(i,j=-infty)^infty((-1)^(i+j))/((i^2+j^2)^s) (1) b_3(2s) = ...

Lauricella functions are generalizations of the Gauss hypergeometric functions to multiple variables. Four such generalizations were investigated by Lauricella (1893), and ...

Let a, b, and c be the lengths of the legs of a triangle opposite angles A, B, and C. Then the law of cosines states a^2 = b^2+c^2-2bccosA (1) b^2 = a^2+c^2-2accosB (2) c^2 = ...

In functional analysis, the Lax-Milgram theorem is a sort of representation theorem for bounded linear functionals on a Hilbert space H. The result is of tantamount ...