What is elliptic integral in math?
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What is elliptic integral in math?
Modern mathematics defines an “elliptic integral” as any function f which can be expressed in the form. where R is a rational function of its two arguments, P is a polynomial of degree 3 or 4 with no repeated roots, and c is a constant.
How do you solve an elliptical integral?
Steps
- Set up the integral to be evaluated.
- Write the integral in terms of the binomial series.
- Evaluate the integral using the Beta function.
- Use Euler’s reflection identity and the fact that Γ ( 1 / 2 ) = π {\displaystyle \Gamma (1/2)={\sqrt {\pi }}} .
- Use the double factorial identity.
- Expand the series.
What are elliptic integrals used for?
Elliptic integrals can be viewed as generalizations of the inverse trigonometric functions and provide solutions to a wider class of problems. For instance, while the arc length of a circle is given as a simple function of the parameter, computing the arc length of an ellipse requires an elliptic integral.
Who discovered elliptic integrals?
Elliptic integrals were intensively studied for many years by the French mathematician Adrien-Marie Legendre, who was able to calculate tables of values for such expressions as functions of their upper endpoint, x. But the topic was completely transformed in the late 1820s by the independent…
What is elliptic integral of first kind?
Abstract. The complete elliptic integral of the first kind K(k) is defined for 0=∫π20dθ√1−k2sin2θ. K ( k ) := ∫ 0 π 2 d θ 1 − k 2 sin 2 The real number k is called the modulus of the elliptic integral.
How do you solve an elliptic integral in Matlab?
K = ellipke( M ) returns the complete elliptic integral of the first kind for each element in M . [ K , E ] = ellipke( M ) returns the complete elliptic integral of the first and second kind. [ K , E ] = ellipke( M , tol ) computes the complete elliptic integral to accuracy tol . The default value of tol is eps .
What is the antiderivative of sin2x?
Answer: The antiderivative of sin2 x is x/ 2 – (sinx cosx) / 2.
What is the integral of Secx?
The integral of sec x is ln|sec x + tan x| + C. It denoted by ∫ sec x dx. This is also known as the antiderivative of sec x.
What is the derivative of sec 2x?
2 sec2x tanx
The derivative of sec^2x is equal to 2 sec2x tanx. It is mathematically written as d(sec^2x)/dx = 2 sec2x tanx.
What is secant used for?
The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.
