Imported Upstream version 1.57.0
[platform/upstream/boost.git] / libs / math / doc / equations / ibeta8.mml
1 <?xml version="1.0" encoding="UTF-8"?>
2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd" [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
3 <html xmlns="http://www.w3.org/1999/xhtml">
4 <head><title>ibeta8</title>
5 <!-- MathML created with MathCast Equation Editor version 0.92 -->
6 </head>
7 <body>
8 <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
9   <mrow>
10      <mtable columnalign="right center left">
11       <mtr>
12         <mtd>
13           <msub>
14             <mi>I</mi>
15             <mi>x</mi>
16           </msub>
17           <mfenced>
18             <mrow>
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20               <mo>,</mo>
21               <mi>b</mi>
22             </mrow>
23           </mfenced>
24         </mtd>
25         <mtd>
26           <mo>&#x2248;</mo>
27         </mtd>
28         <mtd>
29           <mi>M</mi>
30           <munderover>
31             <mo>&#x2211;</mo>
32             <mrow>
33               <mi>n</mi>
34               <mo>=</mo>
35               <mn>0</mn>
36             </mrow>
37             <mi>&#x221e;</mi>
38           </munderover>
39           <msub>
40             <mi>p</mi>
41             <mi>n</mi>
42           </msub>
43           <msub>
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50               <mo>,</mo>
51               <mi>u</mi>
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53           </mfenced>
54           <mspace width="1.0em"/>
55           <mo>;</mo>
56           <mspace width="1.0em"/>
57           <mi>a</mi>
58           <mo>&gt;</mo>
59           <mi>b</mi>
60         </mtd>
61       </mtr>
62       <mtr>
63         <mtd>
64           <mi>M</mi>
65         </mtd>
66         <mtd>
67           <mo>=</mo>
68         </mtd>
69         <mtd>
70           <mfrac>
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72               <mi>H</mi>
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74                 <mrow>
75                   <mi>b</mi>
76                   <mo>,</mo>
77                   <mi>u</mi>
78                 </mrow>
79               </mfenced>
80               <mi>&#x393;</mi>
81               <mfenced>
82                 <mrow>
83                   <mi>a</mi>
84                   <mo>+</mo>
85                   <mi>b</mi>
86                 </mrow>
87               </mfenced>
88             </mrow>
89             <mrow>
90               <mi>&#x393;</mi>
91               <mfenced>
92                 <mrow>
93                   <mi>a</mi>
94                 </mrow>
95               </mfenced>
96               <msup>
97                 <mi>T</mi>
98                 <mi>b</mi>
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101           </mfrac>
102         </mtd>
103       </mtr>
104       <mtr>
105         <mtd>
106           <mi>H</mi>
107           <mfenced>
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109               <mi>c</mi>
110               <mo>,</mo>
111               <mi>u</mi>
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113           </mfenced>
114         </mtd>
115         <mtd>
116           <mo>=</mo>
117         </mtd>
118         <mtd>
119           <mfrac>
120             <mrow>
121               <msup>
122                 <mi>e</mi>
123                 <mrow>
124                   <mo>&#x2212;</mo>
125                   <mi>u</mi>
126                 </mrow>
127               </msup>
128               <msup>
129                 <mi>u</mi>
130                 <mi>c</mi>
131               </msup>
132             </mrow>
133             <mrow>
134               <mi>&#x393;</mi>
135               <mfenced>
136                 <mrow>
137                   <mi>a</mi>
138                 </mrow>
139               </mfenced>
140             </mrow>
141           </mfrac>
142         </mtd>
143       </mtr>
144       <mtr>
145         <mtd>
146           <mi>T</mi>
147         </mtd>
148         <mtd>
149           <mo>=</mo>
150         </mtd>
151         <mtd>
152           <mi>a</mi>
153           <mo>+</mo>
154           <mfrac>
155             <mrow>
156               <mi>b</mi>
157               <mo>&#x2212;</mo>
158               <mn>1</mn>
159             </mrow>
160             <mn>2</mn>
161           </mfrac>
162         </mtd>
163       </mtr>
164       <mtr>
165         <mtd>
166           <mi>u</mi>
167         </mtd>
168         <mtd>
169           <mo>=</mo>
170         </mtd>
171         <mtd>
172           <mo>&#x2212;</mo>
173           <mi>T</mi>
174           <mi>ln</mi>
175           <mfenced>
176             <mrow>
177               <mi>x</mi>
178             </mrow>
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181       </mtr>
182       <mtr>
183         <mtd>
184           <msub>
185             <mi>p</mi>
186             <mn>0</mn>
187           </msub>
188         </mtd>
189         <mtd>
190           <mo>=</mo>
191         </mtd>
192         <mtd>
193           <mn>1</mn>
194         </mtd>
195       </mtr>
196       <mtr>
197         <mtd>
198           <msub>
199             <mi>p</mi>
200             <mi>n</mi>
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202         </mtd>
203         <mtd>
204           <mo>=</mo>
205         </mtd>
206         <mtd>
207           <mfrac>
208             <mrow>
209               <mfenced>
210                 <mrow>
211                   <mi>b</mi>
212                   <mo>&#x2212;</mo>
213                   <mn>1</mn>
214                 </mrow>
215               </mfenced>
216             </mrow>
217             <mrow>
218               <mfenced>
219                 <mrow>
220                   <mn>2</mn>
221                   <mi>n</mi>
222                   <mo>&#x2212;</mo>
223                   <mn>1</mn>
224                 </mrow>
225               </mfenced>
226               <mo>!</mo>
227             </mrow>
228           </mfrac>
229           <mo>+</mo>
230           <mfrac>
231             <mn>1</mn>
232             <mi>n</mi>
233           </mfrac>
234           <munderover>
235             <mo>&#x2211;</mo>
236             <mrow>
237               <mi>m</mi>
238               <mo>=</mo>
239               <mn>1</mn>
240             </mrow>
241             <mrow>
242               <mi>n</mi>
243               <mo>&#x2212;</mo>
244               <mn>1</mn>
245             </mrow>
246           </munderover>
247           <mfrac>
248             <mfenced>
249               <mrow>
250                 <mi>m</mi>
251                 <mi>b</mi>
252                 <mo>&#x2212;</mo>
253                 <mi>n</mi>
254               </mrow>
255             </mfenced>
256             <mrow>
257               <mfenced>
258                 <mrow>
259                   <mn>2</mn>
260                   <mi>m</mi>
261                   <mo>+</mo>
262                   <mn>1</mn>
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264               </mfenced>
265               <mo>!</mo>
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267           </mfrac>
268           <msub>
269             <mi>p</mi>
270             <mrow>
271               <mi>n</mi>
272               <mo>&#x2212;</mo>
273               <mi>m</mi>
274             </mrow>
275           </msub>
276         </mtd>
277       </mtr>
278     </mtable>
279   </mrow>
280 </math></body>
281 </html>