What does EllipticE mean in Mathematica?

EllipticE[m] has a branch cut discontinuity in the complex m plane running from to . EllipticE[ϕ,m] has branch cut discontinuities at and at . For certain special arguments, EllipticE automatically evaluates to exact values. EllipticE can be evaluated to arbitrary numerical precision.

What is K in elliptic integral?

K ( k ) := ∫ 0 π 2 d θ 1 − k 2 sin 2 ⁡ The real number k is called the modulus of the elliptic integral. The complementary modulus is k′=(1−k2)12 k ′ = ( 1 − k 2 ) 1 2 (0

Who invented elliptic functions?

Legendre subsequently studied elliptic integrals and called them elliptic functions. Legendre introduced a three-fold classification –three kinds– which was a crucial simplification of the rather complicated theory at that time.

What does Nabla mean in math?

Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes the standard derivative of the function as defined in calculus.

How did upsilon become Y?

Etymology. The name of the letter was originally just “υ” (y; also called hy, hence “hyoid”, meaning “shaped like the letter υ”), but the name changed to “υ ψιλόν” u psilon ‘simple u’ to distinguish it from οι, which had come to have the same [y] pronunciation.

How do you write gamma in math?

To extend the factorial to any real number x > 0 (whether or not x is a whole number), the gamma function is defined as Γ(x) = Integral on the interval [0, ∞ ] of ∫ 0∞t x −1 e−t dt.

What is elliptice [ m]?

Mathematical function, suitable for both symbolic and numerical manipulation. For and , . . EllipticE [ m] has a branch cut discontinuity in the complex m plane running from to . EllipticE [ ϕ, m] has branch cut discontinuities at and at . For certain special arguments, EllipticE automatically evaluates to exact values.

How do you calculate elliptice?

If one input argument is a scalar and the other one is a vector or a matrix, then ellipticE expands the scalar into a vector or matrix of the same size as the other argument with all elements equal to that scalar. ellipticE (pi/2, m) = ellipticE (m).

Does elliptice automatically evaluate to exact values?

For certain special arguments, EllipticE automatically evaluates to exact values. EllipticE can be evaluated to arbitrary numerical precision. EllipticE automatically threads over lists.

What is elliptic equation?

Elliptic equation, any of a class of partial differential equations describing phenomena that do not change from moment to moment, as when a flow of heat or fluid takes place within a medium with no accumulations.