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The second solution Q_l(x) to the Legendre differential equation. The Legendre functions of the second kind satisfy the same recurrence relation as the Legendre polynomials. ...

The associated Legendre differential equation is a generalization of the Legendre differential equation given by d/(dx)[(1-x^2)(dy)/(dx)]+[l(l+1)-(m^2)/(1-x^2)]y=0, (1) which ...

A transformation from one reference frame to another moving with a constant velocity v with respect to the first for classical motion. However, special relativity shows that ...

An orthogonal transformation is a linear transformation T:V->V which preserves a symmetric inner product. In particular, an orthogonal transformation (technically, an ...

An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of ...

An entire Cremona transformation is a birational transformation of the plane. Cremona transformations are maps of the form x_(i+1) = f(x_i,y_i) (1) y_(i+1) = g(x_i,y_i), (2) ...

Any of the three standard forms in which an elliptic integral can be expressed.

If (1+xsin^2alpha)sinbeta=(1+x)sinalpha, then (1+x)int_0^alpha(dphi)/(sqrt(1-x^2sin^2phi))=int_0^beta(dphi)/(sqrt(1-(4x)/((1+x)^2)sin^2phi)).

A curve and its polar reciprocal with regard to the fixed conic have the same Halphen transformation.

A transformation of the form A^'=UAU^(H), where U^(H) denotes the conjugate transpose.