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```julia
using SpeedyWeather
function SpeedyTransforms.transform_simple!( # SPECTRAL TO GRID
grids::FullGaussianArray, # gridded output
specs::LowerTriangularArray, …
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With mpmath as comparison:
```
sage: import mpmath
sage: from sage.libs.mpmath.all import call as mpcall
sage: mpcall(mpmath.legenp, 29/2, 0, 0)
-0.145632776315886
sage: mpcall(mpmath.legenp, 31…
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One thing that bugs me slightly as the 1.0 release is coming up is the `PiecewiseLegendrePoly` and `PiecewiseLegendreFT` classes.
If, at any point in the future, we want to switch to a different se…
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### Description
There is a wrong output of `jax.scipy.special.sph_harm(m, n, theta, phi, n_max=None)`, when the degree of the harmonic $n \neq 0$.
Here is an example:
```
import jax
import jax.n…
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It appears there is no _legendre function in legendre_ext.c. Can I use legendre_old instead of legendre in utils.py? What's the difference?
Please respond! Very important!
Thank you much
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```Julia
> using ApproxFun
> @time Fun(BigFloat(1),Legendre())
0.000463 seconds (316 allocations: 23.984 KiB)
Fun(Legendre(),BigFloat[1.0])
> @time Fun(1,Chebyshev(BigFloat(-1)..1))
0.000060…
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(bug discovered by making few cleanings in `basic_fun_cl.cpp`)
e.g. :
```
IDL> print, LEGENDRE('.2', [12b,1b],/dou)
-0.18513690 0.20000000
IIDL> print, LEGENDRE(.2, [12b,1b],[1,0],/dou…
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The Legendre polynomials, returned by `legendre_P()`, of the first kind are orthogonal over [-1,1] and are normalized to have value +-1 at the endpoints.
When solving least-squares problems, it's c…
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I got this error:
```
julia> Pl(1.2,3)
DomainError with 1.2:
Legendre Polynomials are defined for arguments lying in -1 ⩽ x ⩽ 1
```
I am somewhat perplexed. A polynomial defined on -1 ⩽ x ⩽ …
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The Gauss-Jacobi quadrature integrates functions of the form
$$
\int_{-1}^1 f(x) (1-x)^\alpha (1+x)^\beta\mathrm{d}x \approx \sum_{i=1}^n w_i f(x_i)
$$
where $\{x_i\}$ are the nodes of $n$-th …