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Given a Taylor series f(x)=f(x_0)+(x-x_0)f^'(x_0)+((x-x_0)^2)/(2!)f^('')(x_0)+... +((x-x_0)^n)/(n!)f^((n))(x_0)+R_n, (1) the error R_n after n terms is given by ...

The Lambert azimuthal equal-area projection is a map projection having transformation equations x = k^'cosphisin(lambda-lambda_0) (1) y = ...

Let lambda be the longitude, lambda_0 the reference longitude, phi the latitude, phi_0 the reference latitude, and phi_1 and phi_2 the standard parallels. Then the ...

An integral transform which is often written as an ordinary Laplace transform involving the delta function. The Laplace transform and Dirichlet series are special cases of ...

The Laplace distribution, also called the double exponential distribution, is the distribution of differences between two independent variates with identical exponential ...

Gamma functions of argument 2z can be expressed in terms of gamma functions of smaller arguments. From the definition of the beta function, ...

Let E(k) and K(k) be complete elliptic integrals of the first and second kinds, with E^'(k) and K^'(k) the complementary integrals. Then ...

The case of the Weierstrass elliptic function with invariants g_2=1 and g_3=0. In this case, the half-periods are given by (omega_1,omega_2)=(omega,iomega), where omega is ...

An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best estimate of the ...

A map projection given by the following transformation, x = lambda-lambda_0 (1) y = 5/4ln[tan(1/4pi+2/5phi)] (2) = 5/4sinh^(-1)[tan(4/5phi)]. (3) Here, x and y are the plane ...