| <?xml version="1.0" encoding="UTF-8"?> |
| <!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'>]> |
| <html xmlns="http://www.w3.org/1999/xhtml"> |
| <head><title>ibeta8</title> |
| <!-- MathML created with MathCast Equation Editor version 0.92 --> |
| </head> |
| <body> |
| <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> |
| <mrow> |
| <mtable columnalign="right center left"> |
| <mtr> |
| <mtd> |
| <msub> |
| <mi>I</mi> |
| <mi>x</mi> |
| </msub> |
| <mfenced> |
| <mrow> |
| <mi>a</mi> |
| <mo>,</mo> |
| <mi>b</mi> |
| </mrow> |
| </mfenced> |
| </mtd> |
| <mtd> |
| <mo>≈</mo> |
| </mtd> |
| <mtd> |
| <mi>M</mi> |
| <munderover> |
| <mo>∑</mo> |
| <mrow> |
| <mi>n</mi> |
| <mo>=</mo> |
| <mn>0</mn> |
| </mrow> |
| <mi>∞</mi> |
| </munderover> |
| <msub> |
| <mi>p</mi> |
| <mi>n</mi> |
| </msub> |
| <msub> |
| <mi>J</mi> |
| <mi>n</mi> |
| </msub> |
| <mfenced> |
| <mrow> |
| <mi>b</mi> |
| <mo>,</mo> |
| <mi>u</mi> |
| </mrow> |
| </mfenced> |
| <mspace width="1.0em"/> |
| <mo>;</mo> |
| <mspace width="1.0em"/> |
| <mi>a</mi> |
| <mo>></mo> |
| <mi>b</mi> |
| </mtd> |
| </mtr> |
| <mtr> |
| <mtd> |
| <mi>M</mi> |
| </mtd> |
| <mtd> |
| <mo>=</mo> |
| </mtd> |
| <mtd> |
| <mfrac> |
| <mrow> |
| <mi>H</mi> |
| <mfenced> |
| <mrow> |
| <mi>b</mi> |
| <mo>,</mo> |
| <mi>u</mi> |
| </mrow> |
| </mfenced> |
| <mi>Γ</mi> |
| <mfenced> |
| <mrow> |
| <mi>a</mi> |
| <mo>+</mo> |
| <mi>b</mi> |
| </mrow> |
| </mfenced> |
| </mrow> |
| <mrow> |
| <mi>Γ</mi> |
| <mfenced> |
| <mrow> |
| <mi>a</mi> |
| </mrow> |
| </mfenced> |
| <msup> |
| <mi>T</mi> |
| <mi>b</mi> |
| </msup> |
| </mrow> |
| </mfrac> |
| </mtd> |
| </mtr> |
| <mtr> |
| <mtd> |
| <mi>H</mi> |
| <mfenced> |
| <mrow> |
| <mi>c</mi> |
| <mo>,</mo> |
| <mi>u</mi> |
| </mrow> |
| </mfenced> |
| </mtd> |
| <mtd> |
| <mo>=</mo> |
| </mtd> |
| <mtd> |
| <mfrac> |
| <mrow> |
| <msup> |
| <mi>e</mi> |
| <mrow> |
| <mo>−</mo> |
| <mi>u</mi> |
| </mrow> |
| </msup> |
| <msup> |
| <mi>u</mi> |
| <mi>c</mi> |
| </msup> |
| </mrow> |
| <mrow> |
| <mi>Γ</mi> |
| <mfenced> |
| <mrow> |
| <mi>a</mi> |
| </mrow> |
| </mfenced> |
| </mrow> |
| </mfrac> |
| </mtd> |
| </mtr> |
| <mtr> |
| <mtd> |
| <mi>T</mi> |
| </mtd> |
| <mtd> |
| <mo>=</mo> |
| </mtd> |
| <mtd> |
| <mi>a</mi> |
| <mo>+</mo> |
| <mfrac> |
| <mrow> |
| <mi>b</mi> |
| <mo>−</mo> |
| <mn>1</mn> |
| </mrow> |
| <mn>2</mn> |
| </mfrac> |
| </mtd> |
| </mtr> |
| <mtr> |
| <mtd> |
| <mi>u</mi> |
| </mtd> |
| <mtd> |
| <mo>=</mo> |
| </mtd> |
| <mtd> |
| <mo>−</mo> |
| <mi>T</mi> |
| <mi>ln</mi> |
| <mfenced> |
| <mrow> |
| <mi>x</mi> |
| </mrow> |
| </mfenced> |
| </mtd> |
| </mtr> |
| <mtr> |
| <mtd> |
| <msub> |
| <mi>p</mi> |
| <mn>0</mn> |
| </msub> |
| </mtd> |
| <mtd> |
| <mo>=</mo> |
| </mtd> |
| <mtd> |
| <mn>1</mn> |
| </mtd> |
| </mtr> |
| <mtr> |
| <mtd> |
| <msub> |
| <mi>p</mi> |
| <mi>n</mi> |
| </msub> |
| </mtd> |
| <mtd> |
| <mo>=</mo> |
| </mtd> |
| <mtd> |
| <mfrac> |
| <mrow> |
| <mfenced> |
| <mrow> |
| <mi>b</mi> |
| <mo>−</mo> |
| <mn>1</mn> |
| </mrow> |
| </mfenced> |
| </mrow> |
| <mrow> |
| <mfenced> |
| <mrow> |
| <mn>2</mn> |
| <mi>n</mi> |
| <mo>−</mo> |
| <mn>1</mn> |
| </mrow> |
| </mfenced> |
| <mo>!</mo> |
| </mrow> |
| </mfrac> |
| <mo>+</mo> |
| <mfrac> |
| <mn>1</mn> |
| <mi>n</mi> |
| </mfrac> |
| <munderover> |
| <mo>∑</mo> |
| <mrow> |
| <mi>m</mi> |
| <mo>=</mo> |
| <mn>1</mn> |
| </mrow> |
| <mrow> |
| <mi>n</mi> |
| <mo>−</mo> |
| <mn>1</mn> |
| </mrow> |
| </munderover> |
| <mfrac> |
| <mfenced> |
| <mrow> |
| <mi>m</mi> |
| <mi>b</mi> |
| <mo>−</mo> |
| <mi>n</mi> |
| </mrow> |
| </mfenced> |
| <mrow> |
| <mfenced> |
| <mrow> |
| <mn>2</mn> |
| <mi>m</mi> |
| <mo>+</mo> |
| <mn>1</mn> |
| </mrow> |
| </mfenced> |
| <mo>!</mo> |
| </mrow> |
| </mfrac> |
| <msub> |
| <mi>p</mi> |
| <mrow> |
| <mi>n</mi> |
| <mo>−</mo> |
| <mi>m</mi> |
| </mrow> |
| </msub> |
| </mtd> |
| </mtr> |
| </mtable> |
| </mrow> |
| </math></body> |
| </html> |