jacobi-roots-0.2.0.4: Roots of two shifted Jacobi polynomials (Legendre and Radau) to double precision

JacobiRoots

Description

Get the roots of shifted Legendre and Radau polynomials

````>>> ````shiftedLegendreRoots 3
```Just (fromList [0.11270166537925831,0.5,0.8872983346207417])
`>>> ````shiftedRadauRoots 2
```Just (fromList [0.1550510257216822,0.6449489742783178])
```

The roots are pre-computed and only a finite number are provided

````>>> ````(V.length allShiftedLegendreRoots, V.length allShiftedRadauRoots)
```(301,301)
`>>> ````shiftedLegendreRoots 1000000000000000
```Nothing
```

There are N roots in the Nth Jacobi polynomial

````>>> ````import Data.Maybe ( fromJust )
````>>> ````V.length (fromJust (shiftedLegendreRoots 5))
```5
`>>> ````all (\k -> k == V.length (fromJust (shiftedLegendreRoots k))) [0..(V.length allShiftedLegendreRoots - 1)]
```True
`>>> ````all (\k -> k == V.length (fromJust (shiftedRadauRoots k))) [0..(V.length allShiftedRadauRoots - 1)]
```True
```

Synopsis

# Documentation

get the roots of the Nth shifted Legendre polynomial

``` `shiftedLegendreRoots` == (`allShiftedLegendreRoots` `!?`)
```
````>>> ````mapM_ (print . shiftedLegendreRoots) [0..3]
```Just (fromList [])
Just (fromList [0.5])
Just (fromList [0.2113248654051871,0.7886751345948129])
Just (fromList [0.11270166537925831,0.5,0.8872983346207417])
```

get the roots of the Nth shifted Radau polynomial

``` `shiftedRadauRoots` == (`allShiftedRadauRoots` `!?`)
```
````>>> ````mapM_ (print . shiftedRadauRoots) [0..3]
```Just (fromList [])
Just (fromList [0.3333333333333333])
Just (fromList [0.1550510257216822,0.6449489742783178])
Just (fromList [8.858795951270394e-2,0.4094668644407347,0.787659461760847])
```

roots of shifted Jacobi polynomials with alpha=0, beta=0

roots of shifted Jacobi polynomials with alpha=1, beta=0