diff options
Diffstat (limited to 'src/algebra/special.spad.pamphlet')
| -rw-r--r-- | src/algebra/special.spad.pamphlet | 12 |
1 files changed, 8 insertions, 4 deletions
diff --git a/src/algebra/special.spad.pamphlet b/src/algebra/special.spad.pamphlet index 8a619f7b..b8c1c293 100644 --- a/src/algebra/special.spad.pamphlet +++ b/src/algebra/special.spad.pamphlet @@ -294,7 +294,8 @@ OrthogonalPolynomialFunctions(R: CommutativeRing): Exports == Impl where laguerreL(n, x) == n = 0 => 1 - (p1, p0) := (-x + 1, 1) + p0: R := 1 + p1: R := -x + 1 for i in 1..n-1 repeat (p1, p0) := ((2*i::R + 1 - x)*p1 - i**2*p0, p1) p1 @@ -312,19 +313,22 @@ OrthogonalPolynomialFunctions(R: CommutativeRing): Exports == Impl where p1 chebyshevT(n, x) == n = 0 => 1 - (p1, p0) := (x, 1) + p0: R := 1 + p1: R := x for i in 1..n-1 repeat (p1, p0) := (2*x*p1 - p0, p1) p1 chebyshevU(n, x) == n = 0 => 1 - (p1, p0) := (2*x, 1) + p0: R := 1 + p1: R := 2*x for i in 1..n-1 repeat (p1, p0) := (2*x*p1 - p0, p1) p1 hermiteH(n, x) == n = 0 => 1 - (p1, p0) := (2*x, 1) + p0: R := 1 + p1: R := 2*x for i in 1..n-1 repeat (p1, p0) := (2*x*p1 - 2*i*p0, p1) p1 |