From 0a1459f1d9bcff32d11026a5b20ab6416020c0ae Mon Sep 17 00:00:00 2001 From: Andreas Schwab Date: Thu, 15 Jun 2023 16:18:58 +0200 Subject: [PATCH] * doc/misc/calc.texi (Advanced Math Functions): Correct calc algebraic syntax. --- doc/misc/calc.texi | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/doc/misc/calc.texi b/doc/misc/calc.texi index 8e42e2ee5d0..de014bf0344 100644 --- a/doc/misc/calc.texi +++ b/doc/misc/calc.texi @@ -18613,7 +18613,7 @@ factorial function: @samp{gamma(n+1) = fact(n)}. For general complex arguments the gamma function can be defined by the following definite integral: @texline @math{\Gamma(a) = \int_0^\infty t^{a-1} e^{-t} dt}. -@infoline @samp{gamma(a) = integ(t@sup{a-1} exp@sup{-t}, t, 0, inf)}. +@infoline @expr{gamma(a) = integ(t^(a-1) exp(-t), t, 0, inf)}. (The actual implementation uses far more efficient computational methods.) @kindex f G @@ -18647,7 +18647,7 @@ The @kbd{f G} (@code{calc-inc-gamma}) [@code{gammaP}] command computes the incomplete gamma function, denoted @samp{P(a,x)}. This is defined by the integral, @texline @math{P(a,x) = \left( \int_0^x t^{a-1} e^t dt \right) / \Gamma(a)}. -@infoline @samp{gammaP(a,x) = integ(t@sup{a-1} e@sup{t}, t, 0, x) / gamma(a)}. +@infoline @expr{gammaP(a,x) = integ(t^(a-1) exp(t), t, 0, x) / gamma(a)}. This implies that @samp{gammaP(a,inf) = 1} for any @expr{a} (see the definition of the normal gamma function). @@ -18682,7 +18682,7 @@ Euler beta function, which is defined in terms of the gamma function as @infoline @expr{beta(a,b) = gamma(a) gamma(b) / gamma(a+b)}, or by @texline @math{B(a,b) = \int_0^1 t^{a-1} (1-t)^{b-1} dt}. -@infoline @samp{beta(a,b) = integ(t@sup{a-1} (1-t)@sup{b-1}, t, 0, 1)}. +@infoline @expr{beta(a,b) = integ(t^(a-1) (1-t)^(b-1), t, 0, 1)}. @kindex f B @kindex H f B @@ -18692,7 +18692,7 @@ or by The @kbd{f B} (@code{calc-inc-beta}) [@code{betaI}] command computes the incomplete beta function @expr{I(x,a,b)}. It is defined by @texline @math{I(x,a,b) = \left( \int_0^x t^{a-1} (1-t)^{b-1} dt \right) / B(a,b)}. -@infoline @samp{betaI(x,a,b) = integ(t@sup{a-1} (1-t)@sup{b-1}, t, 0, x) / beta(a,b)}. +@infoline @expr{betaI(x,a,b) = integ(t^(a-1) (1-t)^(b-1), t, 0, x) / beta(a,b)}. Once again, the @kbd{H} (hyperbolic) prefix gives the corresponding un-normalized version [@code{betaB}]. @@ -18704,7 +18704,7 @@ un-normalized version [@code{betaB}]. The @kbd{f e} (@code{calc-erf}) [@code{erf}] command computes the error function @texline @math{\hbox{erf}(x) = {2 \over \sqrt{\pi}} \int_0^x e^{-t^2} dt}. -@infoline @samp{erf(x) = 2 integ(exp(-(t@sup{2})), t, 0, x) / sqrt(pi)}. +@infoline @expr{erf(x) = 2 integ(exp(-(t^(2))), t, 0, x) / sqrt(pi)}. The complementary error function @kbd{I f e} (@code{calc-erfc}) [@code{erfc}] is the corresponding integral from @samp{x} to infinity; the sum @texline @math{\hbox{erf}(x) + \hbox{erfc}(x) = 1}. -- 2.39.2