Merged updated equations from Trunk.
[SVN r43591]
John Maddock
|
Before Width: | Height: | Size: 1.5 KiB After Width: | Height: | Size: 3.8 KiB |
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Before Width: | Height: | Size: 1.6 KiB After Width: | Height: | Size: 3.9 KiB |
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Before Width: | Height: | Size: 1.6 KiB After Width: | Height: | Size: 3.7 KiB |
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Before Width: | Height: | Size: 4.2 KiB After Width: | Height: | Size: 9.0 KiB |
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Before Width: | Height: | Size: 3.9 KiB After Width: | Height: | Size: 7.3 KiB |
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Before Width: | Height: | Size: 811 B After Width: | Height: | Size: 1.3 KiB |
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Before Width: | Height: | Size: 2.0 KiB After Width: | Height: | Size: 5.1 KiB |
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Before Width: | Height: | Size: 1.4 KiB After Width: | Height: | Size: 2.2 KiB |
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Before Width: | Height: | Size: 2.6 KiB After Width: | Height: | Size: 5.3 KiB |
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Before Width: | Height: | Size: 1.8 KiB After Width: | Height: | Size: 4.1 KiB |
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Before Width: | Height: | Size: 1.2 KiB After Width: | Height: | Size: 2.8 KiB |
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Before Width: | Height: | Size: 1.2 KiB After Width: | Height: | Size: 3.0 KiB |
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Before Width: | Height: | Size: 1.1 KiB After Width: | Height: | Size: 2.6 KiB |
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Before Width: | Height: | Size: 1.1 KiB After Width: | Height: | Size: 2.7 KiB |
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Before Width: | Height: | Size: 2.2 KiB After Width: | Height: | Size: 6.3 KiB |
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Before Width: | Height: | Size: 1.6 KiB After Width: | Height: | Size: 3.8 KiB |
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Before Width: | Height: | Size: 617 B After Width: | Height: | Size: 4.6 KiB |
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Before Width: | Height: | Size: 1.1 KiB After Width: | Height: | Size: 11 KiB |
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Before Width: | Height: | Size: 1.3 KiB After Width: | Height: | Size: 13 KiB |
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Before Width: | Height: | Size: 544 B After Width: | Height: | Size: 3.8 KiB |
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Before Width: | Height: | Size: 649 B After Width: | Height: | Size: 5.1 KiB |
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Before Width: | Height: | Size: 1.4 KiB After Width: | Height: | Size: 4.7 KiB |
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Before Width: | Height: | Size: 497 B After Width: | Height: | Size: 3.0 KiB |
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Before Width: | Height: | Size: 1.3 KiB After Width: | Height: | Size: 3.1 KiB |
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Before Width: | Height: | Size: 853 B After Width: | Height: | Size: 6.6 KiB |
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Before Width: | Height: | Size: 1.6 KiB After Width: | Height: | Size: 11 KiB |
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Before Width: | Height: | Size: 769 B After Width: | Height: | Size: 5.4 KiB |
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Before Width: | Height: | Size: 606 B After Width: | Height: | Size: 4.2 KiB |
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Before Width: | Height: | Size: 922 B After Width: | Height: | Size: 4.0 KiB |
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Before Width: | Height: | Size: 588 B After Width: | Height: | Size: 3.1 KiB |
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Before Width: | Height: | Size: 1.2 KiB After Width: | Height: | Size: 6.5 KiB |
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Before Width: | Height: | Size: 471 B After Width: | Height: | Size: 1.3 KiB |
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Before Width: | Height: | Size: 501 B After Width: | Height: | Size: 1.5 KiB |
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Before Width: | Height: | Size: 766 B After Width: | Height: | Size: 6.1 KiB |
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Before Width: | Height: | Size: 1.2 KiB After Width: | Height: | Size: 6.8 KiB |
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Before Width: | Height: | Size: 807 B After Width: | Height: | Size: 3.9 KiB |
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Before Width: | Height: | Size: 1.0 KiB After Width: | Height: | Size: 4.5 KiB |
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Before Width: | Height: | Size: 1.2 KiB After Width: | Height: | Size: 7.0 KiB |
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Before Width: | Height: | Size: 1.8 KiB After Width: | Height: | Size: 8.3 KiB |
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Before Width: | Height: | Size: 817 B After Width: | Height: | Size: 3.7 KiB |
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Before Width: | Height: | Size: 1.4 KiB After Width: | Height: | Size: 7.3 KiB |
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Before Width: | Height: | Size: 630 B After Width: | Height: | Size: 2.1 KiB |
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Before Width: | Height: | Size: 998 B After Width: | Height: | Size: 1.5 KiB |
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Before Width: | Height: | Size: 2.4 KiB After Width: | Height: | Size: 5.2 KiB |
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Before Width: | Height: | Size: 2.5 KiB After Width: | Height: | Size: 5.6 KiB |
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Before Width: | Height: | Size: 2.0 KiB After Width: | Height: | Size: 4.0 KiB |
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Before Width: | Height: | Size: 3.3 KiB After Width: | Height: | Size: 8.0 KiB |
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Before Width: | Height: | Size: 6.3 KiB After Width: | Height: | Size: 22 KiB |
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Before Width: | Height: | Size: 3.7 KiB After Width: | Height: | Size: 12 KiB |
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Before Width: | Height: | Size: 1.0 KiB After Width: | Height: | Size: 1.9 KiB |
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Before Width: | Height: | Size: 1.7 KiB After Width: | Height: | Size: 13 KiB |
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Before Width: | Height: | Size: 595 B After Width: | Height: | Size: 4.0 KiB |
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Before Width: | Height: | Size: 1.2 KiB After Width: | Height: | Size: 10 KiB |
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Before Width: | Height: | Size: 1.9 KiB After Width: | Height: | Size: 3.8 KiB |
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Before Width: | Height: | Size: 421 B After Width: | Height: | Size: 2.5 KiB |
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Before Width: | Height: | Size: 1.8 KiB After Width: | Height: | Size: 16 KiB |
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Before Width: | Height: | Size: 627 B After Width: | Height: | Size: 4.8 KiB |
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Before Width: | Height: | Size: 1.2 KiB After Width: | Height: | Size: 8.9 KiB |
@@ -27,16 +27,18 @@
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||||
</mfenced>
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||||
</mrow>
|
||||
</msqrt>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mrow>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
</mtd>
|
||||
<mtd>
|
||||
<mo>=</mo>
|
||||
@@ -66,16 +68,18 @@
|
||||
</mfenced>
|
||||
</mrow>
|
||||
</msqrt>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>N</mi>
|
||||
<mo>,</mo>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mrow>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>N</mi>
|
||||
<mo>,</mo>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
</mtd>
|
||||
</mtr>
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||||
<mtr>
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||||
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||||
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Before Width: | Height: | Size: 2.4 KiB After Width: | Height: | Size: 15 KiB |
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Before Width: | Height: | Size: 23 KiB After Width: | Height: | Size: 23 KiB |
@@ -1,15 +1,17 @@
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||||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
||||
<mrow>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mrow>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
<mspace width="1em"/>
|
||||
<mo>=</mo>
|
||||
<mspace width="1em"/>
|
||||
@@ -19,6 +21,44 @@
|
||||
<mi>R</mi>
|
||||
<mi>F</mi>
|
||||
</msub>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<msup>
|
||||
<mi>cos</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<msup>
|
||||
<mi>sin</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mo>+</mo>
|
||||
<mfrac>
|
||||
<mi>n</mi>
|
||||
<mn>3</mn>
|
||||
</mfrac>
|
||||
<mi>sin</mi>
|
||||
<msup>
|
||||
<mi/>
|
||||
<mn>3</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<msub>
|
||||
<mi>R</mi>
|
||||
<mi>J</mi>
|
||||
</msub>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>cos</mi>
|
||||
@@ -41,48 +81,12 @@
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mo>+</mo>
|
||||
<mfrac>
|
||||
<mi>n</mi>
|
||||
<mn>3</mn>
|
||||
</mfrac>
|
||||
<msup>
|
||||
<mi>sin</mi>
|
||||
<mn>3</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<msub>
|
||||
<mi>R</mi>
|
||||
<mi>J</mi>
|
||||
</msub>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<msup>
|
||||
<mi>cos</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1</mn>
|
||||
<mo>−</mo>
|
||||
<msup>
|
||||
<mi>k</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<msup>
|
||||
<mi>sin</mi>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
<mo>,</mo>
|
||||
<mn>1,1</mn>
|
||||
<mo>−</mo>
|
||||
<mi>n</mi>
|
||||
<mi>sin</mi>
|
||||
<msup>
|
||||
<mi>sin</mi>
|
||||
<mi/>
|
||||
<mn>2</mn>
|
||||
</msup>
|
||||
<mi>φ</mi>
|
||||
|
||||
|
Before Width: | Height: | Size: 1.0 KiB After Width: | Height: | Size: 8.9 KiB |
|
Before Width: | Height: | Size: 12 KiB After Width: | Height: | Size: 13 KiB |
@@ -1,13 +1,15 @@
|
||||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
||||
<mrow>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mrow>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
<mspace width="1em"/>
|
||||
<mo>=</mo>
|
||||
<mspace width="1em"/>
|
||||
|
||||
|
Before Width: | Height: | Size: 676 B After Width: | Height: | Size: 4.8 KiB |
|
Before Width: | Height: | Size: 7.3 KiB After Width: | Height: | Size: 7.3 KiB |
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Before Width: | Height: | Size: 1.9 KiB After Width: | Height: | Size: 3.6 KiB |
|
Before Width: | Height: | Size: 2.3 KiB After Width: | Height: | Size: 5.3 KiB |
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Before Width: | Height: | Size: 948 B After Width: | Height: | Size: 1.6 KiB |
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Before Width: | Height: | Size: 2.2 KiB After Width: | Height: | Size: 5.1 KiB |
|
Before Width: | Height: | Size: 2.1 KiB After Width: | Height: | Size: 4.8 KiB |
@@ -1,29 +1,33 @@
|
||||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
||||
<mrow>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
<mo>=</mo>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mrow>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mfrac>
|
||||
<mi>π</mi>
|
||||
<mn>2</mn>
|
||||
</mfrac>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
<mo>=</mo>
|
||||
<mrow>
|
||||
<mo>∏</mo>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<mi>n</mi>
|
||||
<mo>,</mo>
|
||||
<mrow>
|
||||
<mfrac>
|
||||
<mi>π</mi>
|
||||
<mn>2</mn>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
<mo>,</mo>
|
||||
<mi>k</mi>
|
||||
</mrow>
|
||||
</mfenced>
|
||||
</mrow>
|
||||
<mo>=</mo>
|
||||
<msubsup>
|
||||
<mo>∫</mo>
|
||||
|
||||
|
Before Width: | Height: | Size: 2.5 KiB After Width: | Height: | Size: 6.9 KiB |
|
Before Width: | Height: | Size: 9.2 KiB After Width: | Height: | Size: 9.2 KiB |
|
Before Width: | Height: | Size: 2.2 KiB After Width: | Height: | Size: 4.7 KiB |
|
Before Width: | Height: | Size: 1.3 KiB After Width: | Height: | Size: 3.1 KiB |
|
Before Width: | Height: | Size: 1.1 KiB After Width: | Height: | Size: 2.0 KiB |
|
Before Width: | Height: | Size: 1.2 KiB After Width: | Height: | Size: 2.2 KiB |
|
Before Width: | Height: | Size: 264 B After Width: | Height: | Size: 841 B |
|
Before Width: | Height: | Size: 327 B After Width: | Height: | Size: 1.4 KiB |
|
Before Width: | Height: | Size: 766 B After Width: | Height: | Size: 5.6 KiB |
|
Before Width: | Height: | Size: 1.4 KiB After Width: | Height: | Size: 3.2 KiB |
|
Before Width: | Height: | Size: 1.4 KiB After Width: | Height: | Size: 2.7 KiB |
|
Before Width: | Height: | Size: 1.4 KiB After Width: | Height: | Size: 3.1 KiB |
|
Before Width: | Height: | Size: 1.5 KiB After Width: | Height: | Size: 3.3 KiB |
|
Before Width: | Height: | Size: 591 B After Width: | Height: | Size: 3.8 KiB |
@@ -24,29 +24,31 @@
|
||||
</mfenced>
|
||||
<mfenced>
|
||||
<mrow>
|
||||
<munderover>
|
||||
<mo>∑</mo>
|
||||
<mrow>
|
||||
<mn>0</mn>
|
||||
</mrow>
|
||||
<mi>∞</mi>
|
||||
</munderover>
|
||||
<mrow>
|
||||
<mfrac>
|
||||
<msup>
|
||||
<mi>l</mi>
|
||||
<mi>n</mi>
|
||||
</msup>
|
||||
<msup>
|
||||
<mi>a</mi>
|
||||
<mrow>
|
||||
<mover>
|
||||
<mi>n</mi>
|
||||
<mo>−</mo>
|
||||
</mover>
|
||||
</mrow>
|
||||
</msup>
|
||||
</mfrac>
|
||||
<munderover>
|
||||
<mo>∑</mo>
|
||||
<mrow>
|
||||
<mn>0</mn>
|
||||
</mrow>
|
||||
<mi>∞</mi>
|
||||
</munderover>
|
||||
<mrow>
|
||||
<mfrac>
|
||||
<msup>
|
||||
<mi>l</mi>
|
||||
<mi>n</mi>
|
||||
</msup>
|
||||
<msup>
|
||||
<mi>a</mi>
|
||||
<mrow>
|
||||
<mover>
|
||||
<mi>n</mi>
|
||||
<mo>−</mo>
|
||||
</mover>
|
||||
</mrow>
|
||||
</msup>
|
||||
</mfrac>
|
||||
</mrow>
|
||||
</mrow>
|
||||
<mo>+</mo>
|
||||
<mfrac>
|
||||
|
||||
|
Before Width: | Height: | Size: 2.2 KiB After Width: | Height: | Size: 10 KiB |
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 14 KiB |
|
Before Width: | Height: | Size: 1.1 KiB After Width: | Height: | Size: 1.8 KiB |
|
Before Width: | Height: | Size: 1.1 KiB After Width: | Height: | Size: 1.9 KiB |
|
Before Width: | Height: | Size: 1.3 KiB After Width: | Height: | Size: 2.6 KiB |
|
Before Width: | Height: | Size: 570 B After Width: | Height: | Size: 3.4 KiB |
|
Before Width: | Height: | Size: 556 B After Width: | Height: | Size: 3.5 KiB |
|
Before Width: | Height: | Size: 739 B After Width: | Height: | Size: 3.9 KiB |
|
Before Width: | Height: | Size: 966 B After Width: | Height: | Size: 5.8 KiB |
|
Before Width: | Height: | Size: 826 B After Width: | Height: | Size: 4.3 KiB |
|
Before Width: | Height: | Size: 666 B After Width: | Height: | Size: 4.6 KiB |
|
Before Width: | Height: | Size: 458 B After Width: | Height: | Size: 3.3 KiB |