Small corrections to the mathematical functions chapter

Author: mcol

src/functions-reference/mathematical_functions.Rmd

@@ -14,17 +14,18 @@ cat(' * <a href="digamma-appendix.html">Digamma</a>\n')
 
 ## Beta {#beta-appendix}
 
-The beta function, $\text{B}(\alpha,\beta)$, computes the normalizing
+The beta function, $\text{B}(a, b)$, computes the normalizing
 constant for the beta distribution, and is defined for $a > 0$ and $b
 > 0$ by \[ \text{B}(a,b) \ = \ \int_0^1 u^{a - 1} (1 - u)^{b - 1} \,
-du \ = \ \frac{\Gamma(a) \, \Gamma(b)}{\Gamma(a+b)} \, . \]
+du \ = \ \frac{\Gamma(a) \, \Gamma(b)}{\Gamma(a+b)} \, , \]
+where $\Gamma(x)$ is the [Gamma function](#gamma-appendix).
 
 ## Incomplete Beta {#inc-beta-appendix}
 
 The incomplete beta function, $\text{B}(x; a, b)$, is defined for $x
 \in [0, 1]$ and $a, b \geq 0$ such that $a + b \neq 0$ by \[
-\text{B}(x; \, a, b) \ = \ \int_0^x u^{a -  1} \, (1 - u)^{b - 1} \,
-du, `<\] where $\text{B}(a, b)$ is the beta function defined in
+\text{B}(x; \, a, b) \ = \ \int_0^x u^{a - 1} \, (1 - u)^{b - 1} \,
+du, \] where $\text{B}(a, b)$ is the beta function defined in
 [appendix](#beta-appendix).  If $x = 1$, the incomplete beta function
 reduces to the beta function, $\text{B}(1; a, b) = \text{B}(a, b)$.
 
@@ -38,7 +39,7 @@ The gamma function, $\Gamma(x)$, is the generalization of the
 factorial function to continuous variables, defined so that for
 positive integers $n$, \[ \Gamma(n+1) = n! \] Generalizing to all
 positive numbers and non-integer negative numbers, \[ \Gamma(x) =
-\int_0^{\infty} u^{x - 1} \exp(-u) \,n du. \]
+\int_0^{\infty} u^{x - 1} \exp(-u) \, du. \]
 
 ## Digamma {#digamma-appendix}