Rapidly-Converging Series Representations of a Mutual-Information Integral

<table>Evaluation of the two summations in (<a href="https://static.hindawi.com/articles/isrn/volume-2011/546205/figures/#EEq6">6</a>) for <svg height="11.1" id="M121" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 56.037498 11.1" width="56.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜎</tspan>
<tspan style="font-size: 12.50px; " x="10.802592" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.842981" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="29.094481" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="32.22023" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="38.471729" y="0">5</tspan>
</text>
</g>
</g>
</svg>. (a) Value of the summation over <svg height="7.1374998" id="M122" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1375)">
<g transform="translate(72,-66.29)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑚</tspan>
</text>
</g>
</g>
</svg> as a function of the number of terms <svg height="10.325" id="M123" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 17.237499 10.325" width="17.237499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑀</tspan>
</text>
</g>
</g>
</svg>; (b) Value of the summation over <svg height="7.1374998" id="M124" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1375)">
<g transform="translate(72,-66.29)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑛</tspan>
</text>
</g>
</g>
</svg> as a function of the number of terms <svg height="10.325" id="M125" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
</text>
</g>
</g>
</svg>.</table>

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fig3

Figure 3

Figure 3: Rapidly-Converging Series Representations of a Mutual-Information Integral 