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delip

complete and incomplete elliptic integral of first kind

Syntax

r = delip(x, ck)

Arguments

x: real vector/matrix with nonnegative elements
ck: real number between -1 and 1
r: real or complex number (or vector/matrix) with the same size as x

Description

The elliptic integral of the first kind with parameter ck is defined as follow: integral_0^x dt / sqrt((1 - t^2)(1 - c_k^2 t^2))

Where x is real and positive, ck is in [-1 1].

If x is less than 1 the result is real.

When called with x a vector/matrix r is evaluated for each entry of x.

Examples

delip([1,2], 0.5)
deff('y=f(t)','y=1/sqrt((1-t^2)*(1-ck^2*t^2))')
intg(0, 1, f)    // OK since real solution!

See also

amell — Jacobi's am function
ellipj — Jacobi elliptic functions
%k — Jacobi's complete elliptic integral of the first kind (vectorized)

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