# What is Rodrigues formula?

## What is Rodrígues formula?

Rodrigues’ formula. In mathematics, Rodrigues’ formula (formerly called the Ivory–Jacobi formula) is a formula for the Legendre polynomials independently introduced by Olinde Rodrigues (1816), Sir James Ivory (1824) and Carl Gustav Jacobi (1827).

**What is the origin of the Rodrigues’formula?**

In mathematics, Rodrigues’ formula (formerly called the Ivory–Jacobi formula) is a formula for the Legendre polynomials independently introduced by Olinde Rodrigues ( 1816 ), Sir James Ivory ( 1824) and Carl Gustav Jacobi ( 1827 ). The name “Rodrigues formula” was introduced by Heine in 1878,…

**What is Rodrigues’formula for the Legendre function?**

This is Rodrigues’ formula for the Legendre function. By means of the binominal formula we get (28) The summation starts at r=0 and end when n-2ris 0 (n=even) or 1 (n=odd). In evaluating Pnit is most easy to use (27) directly. Thus, .

### What is the Rodrigues formula for Hermite polynomials?

Thus the Rodrigues formula for Hermite polynomials is Rodrigues formula H n(x)=( 1)nex 2dn dxn e (21) We can apply this formula directly to get the ﬁrst few polynomials.

**Is Rodrigues’formula a polynomial of degree n?**

Finally, we need to show that Rodrigues’ formula, Eq. (12.9), results in an expression that is a polynomial of degree n. We note that a typical term of that formula will involve a j -fold differentiation of w and an ( n − j )-fold differentiation of pn.

**How to solve the Legendre polynomials and Rodrigues’formula?**

Legendre polynomials and Rodrigues’ formula Instead of solving the recursion relation (1-54) for the coefficients in the Legendre polynomials, it is easier to use the following trick: Consider the function fn(x)=(x2-1)n. (20) By differentiation we see that it satisfies the following first order differential equation, (1-x2)f’n+2nxfn=0. (21)

#### What is the name of the formula for 3 dimensional rotation?

For the 3-dimensional rotation formula, see Rodrigues’ rotation formula. In mathematics, Rodrigues’ formula (formerly called the Ivory–Jacobi formula) is a formula for the Legendre polynomials independently introduced by Olinde Rodrigues ( 1816 ), Sir James Ivory ( 1824) and Carl Gustav Jacobi ( 1827 ).