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The logarithmic derivative of a function f is defined as the derivative of the logarithm of a function. For example, the digamma function is defined as the logarithmic ...

The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

The application of an apodization function.

A space-filling function.

The most common form of cosine integral is Ci(x) = -int_x^infty(costdt)/t (1) = gamma+lnx+int_0^x(cost-1)/tdt (2) = 1/2[Ei(ix)+Ei(-ix)] (3) = -1/2[E_1(ix)+E_1(-ix)], (4) ...

One of the numbers ..., -2, -1, 0, 1, 2, .... The set of integers forms a ring that is denoted Z. A given integer n may be negative (n in Z^-), nonnegative (n in Z^*), zero ...

A transformation of a hypergeometric function,

where _8phi_7 is a q-hypergeometric function.

_2phi_1(a,q^(-n);c;q,q)=(a^n(c/a,q)_n)/((a;q)_n), where _2phi_1(a,b;c;q,z) is a q-hypergeometric function.

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...