Mercurial > hg > octave-lyh
annotate doc/interpreter/arith.txi @ 16385:a1690c3e93eb
move hook_function constructor to .cc file
* hook-fcn.cc: New file. Move hook_function::hook_function definition
here from hook-fcn.h.
* libinterp/interpfcn/module.mk (INTERPFCN_SRC): Include hook-fcn.cc
in the list.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Thu, 28 Mar 2013 02:52:18 -0400 |
parents | ea2788117ee3 |
children | 2f766ceeb03e |
rev | line source |
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14138
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maint: update copyright notices for 2012
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1 @c Copyright (C) 1996-2012 John W. Eaton |
7018 | 2 @c |
3 @c This file is part of Octave. | |
4 @c | |
5 @c Octave is free software; you can redistribute it and/or modify it | |
6 @c under the terms of the GNU General Public License as published by the | |
7 @c Free Software Foundation; either version 3 of the License, or (at | |
8 @c your option) any later version. | |
9 @c | |
10 @c Octave is distributed in the hope that it will be useful, but WITHOUT | |
11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
13 @c for more details. | |
14 @c | |
15 @c You should have received a copy of the GNU General Public License | |
16 @c along with Octave; see the file COPYING. If not, see | |
17 @c <http://www.gnu.org/licenses/>. | |
3294 | 18 |
4167 | 19 @node Arithmetic |
3294 | 20 @chapter Arithmetic |
21 | |
22 Unless otherwise noted, all of the functions described in this chapter | |
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23 will work for real and complex scalar, vector, or matrix arguments. Functions |
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24 described as @dfn{mapping functions} apply the given operation individually to |
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25 each element when given a matrix argument. For example: |
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26 |
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27 @example |
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28 @group |
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29 sin ([1, 2; 3, 4]) |
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30 @result{} 0.84147 0.90930 |
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31 0.14112 -0.75680 |
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32 @end group |
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33 @end example |
3294 | 34 |
35 @menu | |
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36 * Exponents and Logarithms:: |
3294 | 37 * Complex Arithmetic:: |
38 * Trigonometry:: | |
39 * Sums and Products:: | |
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40 * Utility Functions:: |
3294 | 41 * Special Functions:: |
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42 * Rational Approximations:: |
3803 | 43 * Coordinate Transformations:: |
3294 | 44 * Mathematical Constants:: |
45 @end menu | |
46 | |
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47 @node Exponents and Logarithms |
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48 @section Exponents and Logarithms |
6788 | 49 |
3321 | 50 @DOCSTRING(exp) |
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52 @DOCSTRING(expm1) |
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53 |
3321 | 54 @DOCSTRING(log) |
3294 | 55 |
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56 @DOCSTRING(reallog) |
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57 |
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58 @DOCSTRING(log1p) |
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59 |
3321 | 60 @DOCSTRING(log10) |
3294 | 61 |
3321 | 62 @DOCSTRING(log2) |
3294 | 63 |
3321 | 64 @DOCSTRING(pow2) |
3294 | 65 |
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66 @DOCSTRING(nextpow2) |
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67 |
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68 @DOCSTRING(realpow) |
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69 |
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70 @DOCSTRING(sqrt) |
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71 |
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72 @DOCSTRING(realsqrt) |
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73 |
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74 @DOCSTRING(cbrt) |
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75 |
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76 @DOCSTRING(nthroot) |
3294 | 77 |
4169 | 78 @node Complex Arithmetic |
3294 | 79 @section Complex Arithmetic |
80 | |
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81 In the descriptions of the following functions, |
3294 | 82 @tex |
83 $z$ is the complex number $x + iy$, where $i$ is defined as | |
84 $\sqrt{-1}$. | |
85 @end tex | |
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86 @ifnottex |
3294 | 87 @var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is |
88 defined as @code{sqrt (-1)}. | |
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89 @end ifnottex |
3294 | 90 |
3321 | 91 @DOCSTRING(abs) |
3294 | 92 |
3321 | 93 @DOCSTRING(arg) |
3294 | 94 |
3321 | 95 @DOCSTRING(conj) |
3294 | 96 |
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97 @DOCSTRING(cplxpair) |
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98 |
3321 | 99 @DOCSTRING(imag) |
3294 | 100 |
3321 | 101 @DOCSTRING(real) |
3294 | 102 |
4169 | 103 @node Trigonometry |
3294 | 104 @section Trigonometry |
105 | |
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106 Octave provides the following trigonometric functions where angles are |
6939 | 107 specified in radians. To convert from degrees to radians multiply by |
3294 | 108 @tex |
109 $\pi/180$ | |
110 @end tex | |
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111 @ifnottex |
3294 | 112 @code{pi/180} |
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113 @end ifnottex |
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114 (e.g., @code{sin (30 * pi/180)} returns the sine of 30 degrees). As |
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115 an alternative, Octave provides a number of trigonometric functions |
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116 which work directly on an argument specified in degrees. These functions |
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117 are named after the base trigonometric function with a @samp{d} suffix. For |
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118 example, @code{sin} expects an angle in radians while @code{sind} expects an |
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119 angle in degrees. |
3294 | 120 |
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121 Octave uses the C library trigonometric functions. It is expected that these |
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122 functions are defined by the ISO/IEC 9899 Standard. This Standard is available |
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123 at: @url{http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf}. |
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124 Section F.9.1 deals with the trigonometric functions. The behavior of most of |
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125 the functions is relatively straightforward. However, there are some |
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126 exceptions to the standard behavior. Many of the exceptions involve the |
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127 behavior for -0. The most complex case is atan2. Octave exactly implements |
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128 the behavior given in the Standard. Including |
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129 @tex |
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130 $atan2(\pm0, -0)$ returns $\pm \pi$. |
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131 @end tex |
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132 @ifnottex |
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133 @code{atan2(+- 0, 0)} returns @code{+- pi}. |
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134 @end ifnottex |
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135 |
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136 It should be noted that @sc{matlab} uses different definitions which apparently |
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137 do not distinguish -0. |
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138 |
3321 | 139 @DOCSTRING(sin) |
140 @DOCSTRING(cos) | |
141 @DOCSTRING(tan) | |
142 @DOCSTRING(sec) | |
143 @DOCSTRING(csc) | |
144 @DOCSTRING(cot) | |
3294 | 145 |
3321 | 146 @DOCSTRING(asin) |
147 @DOCSTRING(acos) | |
148 @DOCSTRING(atan) | |
149 @DOCSTRING(asec) | |
150 @DOCSTRING(acsc) | |
151 @DOCSTRING(acot) | |
3294 | 152 |
3321 | 153 @DOCSTRING(sinh) |
154 @DOCSTRING(cosh) | |
155 @DOCSTRING(tanh) | |
156 @DOCSTRING(sech) | |
3428 | 157 @DOCSTRING(csch) |
3321 | 158 @DOCSTRING(coth) |
3294 | 159 |
3321 | 160 @DOCSTRING(asinh) |
161 @DOCSTRING(acosh) | |
162 @DOCSTRING(atanh) | |
163 @DOCSTRING(asech) | |
164 @DOCSTRING(acsch) | |
165 @DOCSTRING(acoth) | |
3294 | 166 |
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167 @DOCSTRING(atan2) |
3294 | 168 |
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169 Octave provides the following trigonometric functions where angles are |
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170 specified in degrees. These functions produce true zeros at the appropriate |
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171 intervals rather than the small round-off error that occurs when using |
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172 radians. For example: |
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173 |
3294 | 174 @example |
175 @group | |
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176 cosd (90) |
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177 @result{} 0 |
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178 cos (pi/2) |
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179 @result{} 6.1230e-17 |
3294 | 180 @end group |
181 @end example | |
182 | |
6502 | 183 @DOCSTRING(sind) |
184 @DOCSTRING(cosd) | |
185 @DOCSTRING(tand) | |
186 @DOCSTRING(secd) | |
187 @DOCSTRING(cscd) | |
188 @DOCSTRING(cotd) | |
189 | |
190 @DOCSTRING(asind) | |
191 @DOCSTRING(acosd) | |
192 @DOCSTRING(atand) | |
193 @DOCSTRING(asecd) | |
194 @DOCSTRING(acscd) | |
195 @DOCSTRING(acotd) | |
3294 | 196 |
4169 | 197 @node Sums and Products |
3294 | 198 @section Sums and Products |
199 | |
3321 | 200 @DOCSTRING(sum) |
3294 | 201 |
3321 | 202 @DOCSTRING(prod) |
3294 | 203 |
3321 | 204 @DOCSTRING(cumsum) |
3294 | 205 |
3321 | 206 @DOCSTRING(cumprod) |
3294 | 207 |
3321 | 208 @DOCSTRING(sumsq) |
3294 | 209 |
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210 @node Utility Functions |
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211 @section Utility Functions |
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212 |
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213 @DOCSTRING(ceil) |
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214 |
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215 @DOCSTRING(fix) |
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216 |
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217 @DOCSTRING(floor) |
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218 |
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219 @DOCSTRING(round) |
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220 |
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221 @DOCSTRING(roundb) |
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222 |
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223 @DOCSTRING(max) |
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224 |
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225 @DOCSTRING(min) |
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226 |
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227 @DOCSTRING(cummax) |
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228 |
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229 @DOCSTRING(cummin) |
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230 |
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231 @DOCSTRING(hypot) |
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232 |
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233 @DOCSTRING(gradient) |
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234 |
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235 @DOCSTRING(dot) |
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236 |
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237 @DOCSTRING(cross) |
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238 |
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239 @DOCSTRING(divergence) |
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240 |
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241 @DOCSTRING(curl) |
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242 |
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243 @DOCSTRING(del2) |
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244 |
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245 @DOCSTRING(factorial) |
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246 |
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247 @DOCSTRING(factor) |
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248 |
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249 @DOCSTRING(gcd) |
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250 |
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251 @DOCSTRING(lcm) |
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252 |
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253 @DOCSTRING(chop) |
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254 |
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255 @DOCSTRING(rem) |
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256 |
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257 @DOCSTRING(mod) |
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258 |
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259 @DOCSTRING(primes) |
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260 |
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261 @DOCSTRING(list_primes) |
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262 |
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263 @DOCSTRING(sign) |
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264 |
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265 @DOCSTRING(signbit) |
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266 |
4169 | 267 @node Special Functions |
3294 | 268 @section Special Functions |
269 | |
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270 @DOCSTRING(airy) |
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272 @DOCSTRING(besselj) |
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3321 | 274 @DOCSTRING(beta) |
3294 | 275 |
3444 | 276 @DOCSTRING(betainc) |
3294 | 277 |
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278 @DOCSTRING(betaincinv) |
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279 |
6502 | 280 @DOCSTRING(betaln) |
281 | |
3321 | 282 @DOCSTRING(bincoeff) |
3294 | 283 |
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284 @DOCSTRING(commutation_matrix) |
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285 |
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286 @DOCSTRING(duplication_matrix) |
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287 |
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288 @DOCSTRING(dawson) |
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289 |
3321 | 290 @DOCSTRING(erf) |
3294 | 291 |
3321 | 292 @DOCSTRING(erfc) |
3294 | 293 |
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294 @DOCSTRING(erfcx) |
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295 |
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296 @DOCSTRING(erfi) |
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297 |
3321 | 298 @DOCSTRING(erfinv) |
3294 | 299 |
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300 @DOCSTRING(erfcinv) |
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301 |
3321 | 302 @DOCSTRING(gamma) |
3294 | 303 |
3444 | 304 @DOCSTRING(gammainc) |
3294 | 305 |
6502 | 306 @DOCSTRING(legendre) |
307 | |
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308 @anchor{doc-gammaln} |
3321 | 309 @DOCSTRING(lgamma) |
310 | |
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311 @node Rational Approximations |
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312 @section Rational Approximations |
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313 |
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314 @DOCSTRING(rat) |
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315 |
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316 @DOCSTRING(rats) |
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317 |
4169 | 318 @node Coordinate Transformations |
3803 | 319 @section Coordinate Transformations |
320 | |
321 @DOCSTRING(cart2pol) | |
322 | |
323 @DOCSTRING(pol2cart) | |
324 | |
325 @DOCSTRING(cart2sph) | |
326 | |
327 @DOCSTRING(sph2cart) | |
328 | |
4169 | 329 @node Mathematical Constants |
3294 | 330 @section Mathematical Constants |
331 | |
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332 @DOCSTRING(e) |
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333 |
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334 @DOCSTRING(pi) |
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335 |
3321 | 336 @DOCSTRING(I) |
337 | |
338 @DOCSTRING(Inf) | |
3294 | 339 |
3321 | 340 @DOCSTRING(NaN) |
3294 | 341 |
3321 | 342 @DOCSTRING(eps) |
3294 | 343 |
3321 | 344 @DOCSTRING(realmax) |
3294 | 345 |
3321 | 346 @DOCSTRING(realmin) |