## 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.