@@ -1010,12 +1010,12 @@ This function generalizes to real numbers using the gamma function.
10101010For $0 \leq y \leq x$, \[ \mathrm{binomial\_ coefficient\_ log}(x,y) =
10111011\log\Gamma(x+1) - \log\Gamma(y+1) - \log\Gamma(x-y+1). \]
10121012
1013- <!-- real; log_falling_factorial; (real x, int n); -->
1014- \index{{\tt \bfseries log\_ falling\_ factorial }!{\tt (real x, int n): real}|hyperpage}
1013+ <!-- real; log_falling_factorial; (real x, real n); -->
1014+ \index{{\tt \bfseries log\_ falling\_ factorial }!{\tt (real x, real n): real}|hyperpage}
10151015
1016- ` real ` ** ` log_falling_factorial ` ** ` (real x, int n) ` <br >\newline
1016+ ` real ` ** ` log_falling_factorial ` ** ` (real x, real n) ` <br >\newline
10171017Return the log of the falling factorial of x with power n defined for
1018- positive x and integer n. \[ \mathrm{log\_ falling\_ factorial}(x,n) =
1018+ positive x and real n. \[ \mathrm{log\_ falling\_ factorial}(x,n) =
10191019\begin{cases} \log (x)_ n & \text{if } x > 0 \\ \textrm{error} &
10201020\text{if } x \leq 0 \end{cases} \]
10211021
@@ -1028,12 +1028,12 @@ and integer n. \[ \mathrm{rising\_factorial}(x,n) = \begin{cases} x^{(n)}
10281028& \text{if } x > 0 \\ \textrm{error} & \text{if } x \leq 0 \end{cases}
10291029\] where \[ x^{(n)}=\frac{\Gamma(x+n)}{\Gamma(x)} \]
10301030
1031- <!-- real; log_rising_factorial; (real x, int n); -->
1031+ <!-- real; log_rising_factorial; (real x, real n); -->
10321032\index{{\tt \bfseries log\_ rising\_ factorial }!{\tt (real x, real n): real}|hyperpage}
10331033
1034- ` real ` ** ` log_rising_factorial ` ** ` (real x, int n) ` <br >\newline
1034+ ` real ` ** ` log_rising_factorial ` ** ` (real x, real n) ` <br >\newline
10351035Return the log of the rising factorial of x with power n defined for
1036- positive x and integer n. \[ \mathrm{log\_ rising\_ factorial}(x,n) =
1036+ positive x and real n. \[ \mathrm{log\_ rising\_ factorial}(x,n) =
10371037\begin{cases} \log x^{(n)} & \text{if } x > 0 \\ \textrm{error} &
10381038\text{if } x \leq 0 \end{cases} \]
10391039
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