Minor docstring fixes

Author: abhro

docs/src/functions_overview.md

@@ -15,17 +15,17 @@ Here the *Special Functions* are listed according to the structure of [NIST Digi
 | [`digamma(x)`](@ref SpecialFunctions.digamma)                        | [digamma function](https://en.wikipedia.org/wiki/Digamma_function) (i.e. the derivative of `loggamma` at `x`)                                                                                        |
 | [`invdigamma(x)`](@ref SpecialFunctions.invdigamma)                  | [invdigamma function](http://bariskurt.com/calculating-the-inverse-of-digamma-function/) (i.e. inverse of `digamma` function at `x` using fixed-point iteration algorithm)                           |
 | [`trigamma(x)`](@ref SpecialFunctions.trigamma)                      | [trigamma function](https://en.wikipedia.org/wiki/Trigamma_function) (i.e the logarithmic second derivative of `gamma` at `x`)                                                                       |
-| [`polygamma(m,x)`](@ref SpecialFunctions.polygamma)                  | [polygamma function](https://en.wikipedia.org/wiki/Polygamma_function) (i.e the (m+1)-th derivative of the `loggamma` function at `x`)                                                               |
+| [`polygamma(m,x)`](@ref SpecialFunctions.polygamma)                  | [polygamma function](https://en.wikipedia.org/wiki/Polygamma_function) (i.e the ``(m+1)``-th derivative of the `loggamma` function at `x`)                                                               |
 | [`gamma(a,z)`](@ref SpecialFunctions.gamma(::Number,::Number))       | [upper incomplete gamma function ``\Gamma(a,z)``](https://en.wikipedia.org/wiki/Incomplete_gamma_function)                                                                                           |
 | [`loggamma(a,z)`](@ref SpecialFunctions.loggamma(::Number,::Number)) | accurate `log(gamma(a,x))` for large arguments                                                                                                                                                       |
-| [`gamma_inc(a,x,IND)`](@ref SpecialFunctions.gamma_inc)              | [incomplete gamma function ratio P(a,x) and Q(a,x)](https://en.wikipedia.org/wiki/Incomplete_gamma_function) (i.e evaluates P(a,x) and Q(a,x) for accuracy specified by IND and returns tuple (p,q)) |
-| [`gamma_inc_inv(a,p,q)`](@ref SpecialFunctions.gamma_inc_inv)        | [inverse of incomplete gamma function ratio P(a,x) and Q(a,x)](https://en.wikipedia.org/wiki/Incomplete_gamma_function) (i.e evaluates x given P(a,x)=p and Q(a,x)=q)                                |
+| [`gamma_inc(a,x,IND)`](@ref SpecialFunctions.gamma_inc)              | [incomplete gamma function ratio ``P(a,x)`` and ``Q(a,x)``](https://en.wikipedia.org/wiki/Incomplete_gamma_function) (i.e evaluates ``P(a,x)`` and ``Q(a,x)`` for accuracy specified by IND and returns tuple (p,q)) |
+| [`gamma_inc_inv(a,p,q)`](@ref SpecialFunctions.gamma_inc_inv)        | [inverse of incomplete gamma function ratio ``P(a,x)`` and ``Q(a,x)``](https://en.wikipedia.org/wiki/Incomplete_gamma_function) (i.e evaluates x given ``P(a,x)=p`` and ``Q(a,x)=q``)                                |
 | [`beta(x,y)`](@ref SpecialFunctions.beta)                            | [beta function](https://en.wikipedia.org/wiki/Beta_function) at `x,y`                                                                                                                                |
 | [`logbeta(x,y)`](@ref SpecialFunctions.logbeta)                      | accurate `log(beta(x,y))` for large `x` or `y`                                                                                                                                                       |
 | [`logabsbeta(x,y)`](@ref SpecialFunctions.logabsbeta)                | accurate `log(abs(beta(x,y)))` for large `x` or `y`                                                                                                                                                  |
 | [`logabsbinomial(x,y)`](@ref SpecialFunctions.logabsbinomial)        | accurate `log(abs(binomial(n,k)))` for large `n` and `k` near `n/2`                                                                                                                                  |
-| [`beta_inc(a,b,x,y)`](@ref SpecialFunctions.beta_inc)                | [incomplete beta function ratio Ix(a,b) and Iy(a,b)](https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function) (i.e evaluates Ix(a,b) and Iy(a,b) and returns tuple (p,q))               |
-| [`beta_inc_inv(a,b,p,q)`](@ref SpecialFunctions.beta_inc_inv)        | Inverse of the incomplete beta function (i.e evaluates x given ``I_{x}(a, b) = p``)                                                                                                                  |
+| [`beta_inc(a,b,x,y)`](@ref SpecialFunctions.beta_inc)                | [incomplete beta function ratio ``I_x(a,b)`` and ``I_y(a,b)``](https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function) (i.e evaluates ``I_x(a,b)`` and ``I_y(a,b)`` and returns tuple (p,q))           |
+| [`beta_inc_inv(a,b,p,q)`](@ref SpecialFunctions.beta_inc_inv)        | Inverse of the incomplete beta function (i.e evaluates ``x`` given ``I_{x}(a, b) = p``)                                                                                                                  |
 
 
 ## Exponential and Trigonometric Integrals

src/bessel.jl

@@ -760,7 +760,7 @@ end
 """
     sphericalbesselj(nu, x)
 
-Spherical bessel function of the first kind at order `nu`, ``j_ν(x)``. This is the non-singular
+Spherical Bessel function of the first kind at order `nu`, ``j_ν(x)``. This is the non-singular
 solution to the radial part of the Helmholz equation in spherical coordinates.
 """
 function sphericalbesselj(nu, x::T) where {T}
@@ -775,7 +775,7 @@ end
 """
     sphericalbessely(nu, x)
 
-Spherical bessel function of the second kind at order `nu`, ``y_ν(x)``. This is
+Spherical Bessel function of the second kind at order `nu`, ``y_ν(x)``. This is
 the singular solution to the radial part of the Helmholz equation in spherical
 coordinates. Sometimes known as a spherical Neumann function.
 """

src/gamma.jl

@@ -227,7 +227,7 @@ Generalized zeta function defined by
 ```math
 \zeta(s, z) = \sum_{k=0}^\infty \frac{1}{((k+z)^2)^{s/2}},
 ```
-where any term with ``k+z = 0`` is excluded.  For ``\Re z > 0``,
+where any term with ``k+z = 0`` is excluded.  For ``\Re(z) > 0``,
 this definition is equivalent to the Hurwitz zeta function
 ``\sum_{k=0}^\infty (k+z)^{-s}``.
 

src/gamma_inc.jl

@@ -543,7 +543,7 @@ end
 @doc raw"""
     gamma_inc_minimax(a,x,z)
 
-Compute ``P(a,x)`` using minimax approximations given by :
+Compute ``P(a,x)`` using minimax approximations given by:
 ```math
 1/2 * \operatorname{erfc}(\sqrt{y}) - e^{-y}/\sqrt{2\pi a} ⋅ T(a,\lambda)
 ``` where