Merge pull request #17841 from JuliaLang/ksh/docspecial

Move trig and gamma docs out of helpDB, make them less verbose.

base/docs/helpdb/Base.jl

@@ -22,13 +22,6 @@ tab-delimited text to `f` by either `writedlm(f, [x y])` or by `writedlm(f, zip(
 """
 writedlm
 
-"""
-    digamma(x)
-
-Compute the digamma function of `x` (the logarithmic derivative of `gamma(x)`)
-"""
-digamma
-
 """
     fill!(A, x)
 
@@ -523,13 +516,6 @@ A string giving the literal bit representation of a number.
 """
 bits
 
-"""
-    invdigamma(x)
-
-Compute the inverse digamma function of `x`.
-"""
-invdigamma
-
 """
     getindex(type[, elements...])
 
@@ -609,13 +595,6 @@ used as the final delimiter instead of `delim`.
 """
 join(io, items, delim, last)
 
-"""
-    lfact(x)
-
-Compute the logarithmic factorial of `x`
-"""
-lfact
-
 """
     deconv(b,a)
 
@@ -1007,15 +986,6 @@ Test whether a matrix is lower triangular.
 """
 istril
 
-"""
-    lgamma(x)
-
-Compute the logarithm of the absolute value of [`gamma`](:func:`gamma`) for
-[`Real`](:obj:`Real`) `x`, while for [`Complex`](:obj:`Complex`) `x` it computes the
-logarithm of `gamma(x)`.
-"""
-lgamma
-
 """
     bin(n, [pad])
 
@@ -1445,13 +1415,6 @@ Close an I/O stream. Performs a `flush` first.
 """
 close(stream::IO)
 
-"""
-    cospi(x)
-
-Compute ``\\cos(\\pi x)`` more accurately than `cos(pi*x)`, especially for large `x`.
-"""
-cospi
-
 """
     parentindexes(A)
 
@@ -2420,13 +2383,6 @@ Bessel function of the first kind of order 1, ``J_1(x)``.
 """
 besselj1
 
-"""
-    sinpi(x)
-
-Compute ``\\sin(\\pi x)`` more accurately than `sin(pi*x)`, especially for large `x`.
-"""
-sinpi
-
 """
     select!(v, k, [by=<transform>,] [lt=<comparison>,] [rev=false])
 
@@ -2872,13 +2828,6 @@ Seek a stream to the given position.
 """
 seek
 
-"""
-    acosd(x)
-
-Compute the inverse cosine of `x`, where the output is in degrees.
-"""
-acosd
-
 """
     triu(M)
 
@@ -3013,13 +2962,6 @@ Equivalent to `stat(file).size`.
 """
 filesize
 
-"""
-    sinc(x)
-
-Compute ``\\sin(\\pi x) / (\\pi x)`` if ``x \\neq 0``, and ``1`` if ``x = 0``.
-"""
-sinc
-
 """
     cglobal((symbol, library) [, type=Void])
 
@@ -3650,13 +3592,6 @@ Returns the smallest eigenvalue of `A`.
 """
 eigmin
 
-"""
-    acscd(x)
-
-Compute the inverse cosecant of `x`, where the output is in degrees.
-"""
-acscd
-
 """
     ltoh(x)
 
@@ -4142,13 +4077,6 @@ is `-1` the corresponding ID will not change. Only integer `owner`s and `group`s
 """
 chown
 
-"""
-    gamma(x)
-
-Compute the gamma function of `x`.
-"""
-gamma
-
 """
     sin(x)
 
@@ -4855,13 +4783,6 @@ For more information, see [^issue8859], [^B96], [^S84], [^KY88].
 """
 pinv
 
-"""
-    asecd(x)
-
-Compute the inverse secant of `x`, where the output is in degrees.
-"""
-asecd
-
 """
     readbytes!(stream::IO, b::AbstractVector{UInt8}, nb=length(b); all=true)
 
@@ -4888,13 +4809,6 @@ descriptive error string.
 """
 ArgumentError
 
-"""
-    atand(x)
-
-Compute the inverse tangent of `x`, where the output is in degrees.
-"""
-atand
-
 """
     KeyError(key)
 
@@ -5062,13 +4976,6 @@ Test whether a matrix is Hermitian.
 """
 ishermitian
 
-"""
-    sind(x)
-
-Compute sine of `x`, where `x` is in degrees.
-"""
-sind
-
 """
     min(x, y, ...)
 
@@ -5380,14 +5287,6 @@ two strings. For example
 """
 join(strings, delim, last)
 
-"""
-    polygamma(m, x)
-
-Compute the polygamma function of order `m` of argument `x` (the `(m+1)th` derivative of the
-logarithm of `gamma(x)`)
-"""
-polygamma
-
 """
     isless(x, y)
 
@@ -6055,13 +5954,6 @@ Returns `string` with all characters converted to uppercase.
 """
 uppercase
 
-"""
-    cosd(x)
-
-Compute cosine of `x`, where `x` is in degrees.
-"""
-cosd
-
 """
     cycle(iter)
 
@@ -6500,13 +6392,6 @@ lengths of dimensions you asked for.
 """
 size
 
-"""
-    trigamma(x)
-
-Compute the trigamma function of `x` (the logarithmic second derivative of `gamma(x)`).
-"""
-trigamma
-
 """
     findmin(A, dims) -> (minval, index)
 
@@ -7188,13 +7073,6 @@ but throws an error for unordered arguments.
 """
 cmp
 
-"""
-    tand(x)
-
-Compute tangent of `x`, where `x` is in degrees.
-"""
-tand
-
 """
     issorted(v, [by=<transform>,] [lt=<comparison>,] [rev=false])
 
@@ -7583,14 +7461,6 @@ Test whether any values along the given dimensions of an array are `true`.
 """
 any(::AbstractArray,dims)
 
-"""
-    cosc(x)
-
-Compute ``\\cos(\\pi x) / x - \\sin(\\pi x) / (\\pi x^2)`` if ``x \\neq 0``, and ``0`` if
-``x = 0``. This is the derivative of `sinc(x)`.
-"""
-cosc
-
 """
     getkey(collection, key, default)
 
@@ -7612,13 +7482,6 @@ For matrices or vectors ``A`` and ``B``, calculates ``Aᴴ Bᴴ``.
 """
 Ac_mul_Bc
 
-"""
-    acotd(x)
-
-Compute the inverse cotangent of `x`, where the output is in degrees.
-"""
-acotd
-
 """
     zeros(type, dims)
 
@@ -8313,13 +8176,6 @@ julia> f(apple)
 """
 :@enum
 
-"""
-    asind(x)
-
-Compute the inverse sine of `x`, where the output is in degrees.
-"""
-asind
-
 """
     widemul(x, y)
 

base/special/gamma.jl

@@ -2,6 +2,12 @@
 
 gamma(x::Float64) = nan_dom_err(ccall((:tgamma,libm),  Float64, (Float64,), x), x)
 gamma(x::Float32) = nan_dom_err(ccall((:tgammaf,libm),  Float32, (Float32,), x), x)
+
+"""
+    gamma(x)
+
+Compute the gamma function of `x`.
+"""
 gamma(x::Real) = gamma(float(x))
 @vectorize_1arg Number gamma
 
@@ -19,6 +25,11 @@ lgamma_r(x::Real) = lgamma_r(float(x))
 lgamma_r(x::Number) = lgamma(x), 1 # lgamma does not take abs for non-real x
 "`lgamma_r(x)`: return L,s such that `gamma(x) = s * exp(L)`" lgamma_r
 
+"""
+    lfact(x)
+
+Compute the logarithmic factorial of `x`
+"""
 lfact(x::Real) = (x<=1 ? zero(float(x)) : lgamma(x+one(x)))
 @vectorize_1arg Number lfact
 
@@ -47,6 +58,13 @@ function clgamma_lanczos(z)
     return log(zz) - temp
 end
 
+"""
+    lgamma(x)
+
+Compute the logarithm of the absolute value of [`gamma`](:func:`gamma`) for
+[`Real`](:obj:`Real`) `x`, while for [`Complex`](:obj:`Complex`) `x` it computes the
+logarithm of `gamma(x)`.
+"""
 function lgamma(z::Complex)
     if real(z) <= 0.5
         a = clgamma_lanczos(1-z)
@@ -69,6 +87,11 @@ gamma(z::Complex) = exp(lgamma(z))
 #   const A002445 = [1,6,30,42,30,66,2730,6,510,798,330,138,2730,6,870,14322,510,6,1919190,6,13530]
 #   const bernoulli = A000367 .// A002445 # even-index Bernoulli numbers
 
+"""
+    digamma(x)
+
+Compute the digamma function of `x` (the logarithmic derivative of `gamma(x)`)
+"""
 function digamma(z::Union{Float64,Complex{Float64}})
     # Based on eq. (12), without looking at the accompanying source
     # code, of: K. S. Kölbig, "Programs for computing the logarithm of
@@ -98,6 +121,11 @@ function digamma(z::Union{Float64,Complex{Float64}})
     ψ -= t * @evalpoly(t,0.08333333333333333,-0.008333333333333333,0.003968253968253968,-0.004166666666666667,0.007575757575757576,-0.021092796092796094,0.08333333333333333,-0.4432598039215686)
 end
 
+"""
+    trigamma(x)
+
+Compute the trigamma function of `x` (the logarithmic second derivative of `gamma(x)`).
+"""
 function trigamma(z::Union{Float64,Complex{Float64}})
     # via the derivative of the Kölbig digamma formulation
     x = real(z)
@@ -360,6 +388,12 @@ function zeta(s::Union{Int,Float64,Complex{Float64}},
     return ζ
 end
 
+"""
+    polygamma(m, x)
+
+Compute the polygamma function of order `m` of argument `x` (the `(m+1)th` derivative of the
+logarithm of `gamma(x)`)
+"""
 function polygamma(m::Integer, z::Union{Float64,Complex{Float64}})
     m == 0 && return digamma(z)
     m == 1 && return trigamma(z)
@@ -445,6 +479,12 @@ function invdigamma(y::Float64)
     return x_new
 end
 invdigamma(x::Float32) = Float32(invdigamma(Float64(x)))
+
+"""
+    invdigamma(x)
+
+Compute the inverse digamma function of `x`.
+"""
 invdigamma(x::Real) = invdigamma(Float64(x))
 @vectorize_1arg Real invdigamma