Legendre, Hermite, Laguerre, Chebyshev polynomials

Project.toml

@@ -1,21 +1,22 @@
-name = "SpecialFunctions"
-uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
+name  = "SpecialFunctions"
+uuid  = "276daf66-3868-5448-9aa4-cd146d93841b"
 version = "1.2.1"
 
 [deps]
-ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+ChainRulesCore  = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 OpenSpecFun_jll = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
 
 [compat]
-ChainRulesCore = "0.9"
+ChainRulesCore  = "0.9"
 ChainRulesTestUtils = "0.5.10, 0.6"
-OpenSpecFun_jll = "0.5"
-julia = "1.3"
+OpenSpecFun_jll  = "0.5"
+julia  = "1.3"
 
 [extras]
 ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
-Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["ChainRulesTestUtils", "Random", "Test"]
+test = ["ChainRulesTestUtils", "Polynomials", "Random", "Test"]

docs/src/functions_list.md

@@ -69,4 +69,10 @@ SpecialFunctions.beta
 SpecialFunctions.logbeta
 SpecialFunctions.logabsbeta
 SpecialFunctions.logabsbinomial
+SpecialFunctions.chebyshevt
+SpecialFunctions.chebyshevu
+SpecialFunctions.hermiteh
+SpecialFunctions.laguerrel
+SpecialFunctions.legendrep
+SpecialFunctions.legendreq
 ```

docs/src/functions_overview.md

@@ -82,6 +82,18 @@ Here the *Special Functions* are listed according to the structure of [NIST Digi
 | [`besselkx(nu,z)`](@ref SpecialFunctions.besselkx) | scaled modified Bessel function of the second kind of order `nu` at `z` |
 | [`jinc(x)`](@ref SpecialFunctions.jinc) | scaled [Bessel function of the first kind divided by `x`](https://en.wikipedia.org/wiki/Sombrero_function). A.k.a. sombrero or besinc |
 
+## [Legendre and Related Functions](https://dlmf.nist.gov/14)
+| Function | Description |
+|:-------- |:----------- |
+| [`chebyshevt(n,x)`](@ref SpecialFunctions.chebyshevt) | [Chebyshev polynomial of the first kind](https://en.wikipedia.org/wiki/Chebyshev_polynomials) ``T_n(x)`` |
+| [`chebyshevu(n,x)`](@ref SpecialFunctions.chebyshevu) | [Chebyshev polynomial of the second kind](https://en.wikipedia.org/wiki/Chebyshev_polynomials) ``U_n(x)`` |
+| [`hermiteh(n,x)`](@ref SpecialFunctions.hermiteh) | [Hermite polynomial](https://en.wikipedia.org/wiki/Hermite_polynomials) ``H_n(x)`` |
+| [`laguerrel(n,x)`](@ref SpecialFunctions.laguerrel) | [Laguerre polynomial](https://en.wikipedia.org/wiki/Laguerre_polynomials) ``L_n(x)`` |
+| [`legendrep(n,x)`](@ref SpecialFunctions.legendrep) | [Legendre polynomial](https://en.wikipedia.org/wiki/Legendre_polynomials) ``P_n(x)`` |
+| [`legendrep(n,m,x)`](@ref SpecialFunctions.legendrep) | [Associated Legendre function of the first kind](https://en.wikipedia.org/wiki/Associated_Legendre_polynomials) ``P_n^{(m)}(x)`` |
+| [`legendreq(n,x)`](@ref SpecialFunctions.legendreq) | [Legendre function of the second kind](https://en.wikipedia.org/wiki/Legendre_function#Legendre_functions_of_the_second_kind_(Qn)) ``Q_n(x)`` |
+| [`legendreq(n,m,x)`](@ref SpecialFunctions.legendreq) | [Associated Legendre function of the second kind](https://en.wikipedia.org/wiki/Legendre_function#Associated_Legendre_functions_of_the_second_kind) ``Q_n^{(m)}(x)`` |
+
 
 ## [Elliptic Integrals](https://dlmf.nist.gov/19)
 | Function | Description |