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Let u_(p) be a unit tangent vector of a regular surface M subset R^3. Then the normal curvature of M in the direction u_(p) is kappa(u_(p))=S(u_(p))·u_(p), (1) where S is the ...

The Weingarten equations express the derivatives of the normal vector to a surface using derivatives of the position vector. Let x:U->R^3 be a regular patch, then the shape ...

The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a ...

A Bessel function of the second kind Y_n(x) (e.g, Gradshteyn and Ryzhik 2000, p. 703, eqn. 6.649.1), sometimes also denoted N_n(x) (e.g, Gradshteyn and Ryzhik 2000, p. 657, ...

The curl of a vector field, denoted curl(F) or del xF (the notation used in this work), is defined as the vector field having magnitude equal to the maximum "circulation" at ...

The n-roll mill curve is given by the equation x^n-(n; 2)x^(n-2)y^2+(n; 4)x^(n-4)y^4-...=a^n, where (n; k) is a binomial coefficient.

Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) (1) is the multinomial coefficient ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

The system of partial differential equations del ^4u = E(v_(xy)^2-v_(xx)v_(yy)) (1) del ^4v = alpha+beta(u_(yy)v_(xx)+u_(xx)v_(yy)-2u_(xy)v_(xy)), (2) where del ^4 is the ...

Let four lines in a plane represent four roads in general position, and let one traveler T_i be walking along each road at a constant (but not necessarily equal to any other ...