[cl-gsl-cvs] CVS update: cl-gsl/doc/sf.tex
Edgar Denny
edenny at common-lisp.net
Thu Mar 24 03:48:44 UTC 2005
Update of /project/cl-gsl/cvsroot/cl-gsl/doc
In directory common-lisp.net:/tmp/cvs-serv6348
Modified Files:
sf.tex
Log Message:
Convert more of the math to images.
Date: Thu Mar 24 04:48:43 2005
Author: edenny
Index: cl-gsl/doc/sf.tex
diff -u cl-gsl/doc/sf.tex:1.1 cl-gsl/doc/sf.tex:1.2
--- cl-gsl/doc/sf.tex:1.1 Mon Mar 21 04:44:31 2005
+++ cl-gsl/doc/sf.tex Thu Mar 24 04:48:41 2005
@@ -7,16 +7,17 @@
\Css{.monobold { font-weight: bold; font-family: monospace;}}
\Css{.floatright { float: right;}}
+\Css{.floatleft { float: left;}}
+\Css{.floatclear { clear: both;}}
\def\monobf#1{\ifHtml \HCode{<span class="monobold">} #1
\else \textbf{\texttt{#1}} \fi
\ifHtml \HCode{</span>} \fi}
\def\func#1#2{\ifHtml \HCode{<span class="floatright">} \fi
- {[}Function{]} \ifHtml \HCode{</span>} \fi
- \monobf{#1} \texttt{#2}}
-
-\setcounter{section}{6}
+ {[}Function{]} \ifHtml \HCode{</span><span class="floatleft">} \fi
+ \monobf{#1} \texttt{#2}
+ \ifHtml \HCode{</span> <div class="floatclear"> </div>} \fi}
\section{Special Functions}
@@ -81,12 +82,12 @@
The following precision levels are available for the mode argument,
\begin{description}
-\item [GSL\_PREC\_DOUBLE~]Double-precision, a relative accuracy of approximately
- 2 {*} 10\^{}-16.
-\item [GSL\_PREC\_SINGLE~]Single-precision, a relative accuracy of approximately
- 10\^{}-7.
-\item [GSL\_PREC\_APPROX~]Approximate values, a relative accuracy of
-approximately 5 {*} 10\^{}-4.
+\item [+prec-double+] Double-precision, a relative accuracy of approximately
+ \(2 * 10^{-16}\).
+\item [+prec-single+] Single-precision, a relative accuracy of approximately
+ \(10^{-1}\).
+\item [+prec-approx+] Approximate values, a relative accuracy of
+approximately \(5 * 10^{-4}\).
\end{description}
The approximate mode provides the fastest evaluation at the lowest
accuracy.
@@ -94,47 +95,47 @@
\subsection{Airy Functions and Derivatives}
-The Airy functions Ai(x) and Bi(x) are defined by the integral representations,
-For further information see Abramowitz \& Stegun, Section 10.4.
-The \HCode{<span class="mystyle">} Airy functions \HCode{</span>} are defined in the header file gsl\_sf\_airy.h.
+The Airy functions \(Ai(x)\) and \(Bi(x)\) are defined by the integral
+representations,
-\subsubsection{Airy Functions}
+$$Ai(x) = \frac{1}{\pi} \int_0^\infty \cos(\frac{1}{3} t^3 + xt) dt$$
+
+$$Bi(x) = \frac{1}{\pi} \int_0^\infty (e^{-t^3/3} + \sin(\frac{1}{3} t^3 + xt)) dt$$
+for further information see Abramowitz \& Stegun, Section 10.4.
+
+\subsubsection{Airy Functions}
\func{airy-ai}{x mode => result}
\func{airy-ai-e}{x mode => result, error, status}
-These routines compute the Airy function Ai(x) with an accuracy
+These routines compute the Airy function \(Ai(x)\) with an accuracy
specified by mode.
\func{airy-bi}{x mode => result}
\func{airy-bi-e}{x mode => result, error, status}
-These routines compute the Airy function Bi(x) with an accuracy
+These routines compute the Airy function \(Bi(x)\) with an accuracy
specified by mode.
\func{airy-ai-scaled}{ x mode => result}
-
\func{airy-ai-scaled-e}{ x mode => result, error, status}
-
These routines compute a scaled version of the Airy function
-S\_A(x) Ai(x). For x>0 the scaling factor S\_A(x) is $\backslash$exp(+(2/3)
-x\^{}(3/2)), and is 1 for x<0.
+\(S_A(x) Ai(x)\). For \(x>0\) the scaling factor \(S_A(x)\) is
+\(e^{+(2/3)x^{3/2}}\), and is 1 for \(x<0\).
\func{airy-bi-scaled}{ x mode => result}
-
\func{airy-bi-scaled-e}{ x mode => result, error, status}
-
These routines compute a scaled version of the Airy function
-S\_B(x) Bi(x). For x>0 the scaling factor S\_B(x) is exp(-(2/3) x\^{}(3/2)),
-and is 1 for x<0.
+\(S_B(x) Bi(x)\). For \(x>0\) the scaling factor \(S_B(x)\) is
+\(e^{-(2/3) x^{3/2}}\), and is 1 for \(x<0\).
\subsubsection{Derivatives of Airy Functions}
@@ -145,7 +146,7 @@
\func{airy-ai-deriv-e}{ x mode => result, error, status}
-These routines compute the Airy function derivative Ai\verb|'|(x)
+These routines compute the Airy function derivative \(Ai'(x)\)
with an accuracy specified by mode.
\func{airy-bi-deriv}{ x mode => result}
@@ -154,7 +155,7 @@
\func{airy-bi-deriv-e}{ x mode => result, error, status}
-These routines compute the Airy function derivative Bi\verb|'|(x)
+These routines compute the Airy function derivative \(Bi'(x)\)
with an accuracy specified by mode.
\func{airy-ai-deriv-scaled}{ x mode => result}
@@ -163,7 +164,7 @@
These routines compute the derivative of the scaled Airy function
-S\_A(x) Ai(x).
+\(S_A(x) Ai(x)\).
\func{airy-bi-deriv-scaled}{ x mode => result}
@@ -172,7 +173,7 @@
These routines compute the derivative of the scaled Airy function
-S\_B(x) Bi(x).
+\(S_B(x) Bi(x)\).
\subsubsection{Zeros of Airy Functions}
@@ -184,7 +185,7 @@
These routines compute the location of the s-th zero of the
-Airy function Ai(x).
+Airy function \(Ai(x)\).
\func{airy-zero-bi}{ s => result}
@@ -193,7 +194,7 @@
These routines compute the location of the s-th zero of the
-Airy function Bi(x).
+Airy function \(Bi(x)\).
\subsubsection{Zeros of Derivatives of Airy Functions}
@@ -205,7 +206,7 @@
These routines compute the location of the s-th zero of the
-Airy function derivative Ai\verb|'|(x).
+Airy function derivative \(Ai'(x)\).
\func{airy-zero-bi-deriv}{ s => result}
@@ -214,7 +215,7 @@
These routines compute the location of the s-th zero of the
-Airy function derivative Bi\verb|'|(x).
+Airy function derivative \(Bi'(x)\).
\subsection{Bessel Functions}
@@ -260,7 +261,8 @@
This routine computes the values of the regular cylindrical
-Bessel functions \(J_n(x)\) for n from nmin to nmax inclusive, storing
+Bessel functions \(J_n(x)\) for \texttt{n} from \texttt{nmin} to
+\texttt{nmax} inclusive, storing
the results in the array result-array. The values are computed using
recurrence relations, for efficiency, and therefore may differ slightly
from the exact values.
@@ -299,7 +301,8 @@
This routine computes the values of the irregular cylindrical
-Bessel functions \(Y_n(x)\) for n from nmin to nmax inclusive, storing
+Bessel functions \(Y_n(x)\) for \texttt{n} from \texttt{nmin}
+to \texttt{nmax} inclusive, storing
the results in the array result-array.
The domain of the function is \(x>0\).
The values are computed using recurrence relations, for efficiency,
@@ -339,7 +342,8 @@
This routine computes the values of the regular modified cylindrical
-Bessel functions \(I_n(x)\) for n from nmin to nmax inclusive, storing
+Bessel functions \(I_n(x)\) for \texttt{n} from \texttt{nmin} to
+\texttt{nmax} inclusive, storing
the results in the array result-array. The start of the range nmin
must be positive or zero. The values are computed using recurrence
relations, for efficiency, and therefore may differ slightly from
@@ -376,8 +380,8 @@
This routine computes the values of the scaled regular cylindrical
-Bessel functions \(e^{-|x|} I_n(x)\) for n from nmin to
-nmax inclusive, storing the results in the array result-array. The
+Bessel functions \(e^{-|x|} I_n(x)\) for \texttt{n} from \texttt{nmin} to
+\texttt{nmax} inclusive, storing the results in the array result-array. The
start of the range nmin must be positive or zero. The values are computed
using recurrence relations, for efficiency, and therefore may differ
slightly from the exact values.
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