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    <title>MaplePrimes - answers and comments on Question, error recursive equation but it is not recursive</title>
    <link>http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive</link>
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    <copyright>2026 Maplesoft, A Division of Waterloo Maple Inc.</copyright>
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    <lastBuildDate>Tue, 09 Jun 2026 07:18:45 GMT</lastBuildDate>
    <pubDate>Tue, 09 Jun 2026 07:18:45 GMT</pubDate>
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    <itunes:summary />
    <description>The latest answers and comments added to the Question, error recursive equation but it is not recursive</description>
    <image>
      <url>http://www.mapleprimes.com/images/mapleprimeswhite.jpg</url>
      <title>MaplePrimes - answers and comments on Question, error recursive equation but it is not recursive</title>
      <link>http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive</link>
    </image>
    <item>
      <title>Syntax error</title>
      <link>http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive?ref=Feed:MaplePrimes:error recursive equation but it is not recursive:Comments#answer143163</link>
      <itunes:summary>&lt;p&gt;A semicolon is missing after the assignment to network.&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;A semicolon is missing after the assignment to network.&lt;/p&gt;</description>
      <guid>143163</guid>
      <pubDate>Wed, 06 Feb 2013 18:47:47 Z</pubDate>
      <itunes:author>Preben Alsholm</itunes:author>
      <author>Preben Alsholm</author>
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    <item>
      <title>Works for concrete i</title>
      <link>http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive?ref=Feed:MaplePrimes:error recursive equation but it is not recursive:Comments#answer143164</link>
      <itunes:summary>&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;form name="worksheet_form"&gt;
&lt;table style="width: 576px;" align="center"&gt;
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&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -78;" src="/view.aspx?sf=143164/453331/9917c1e2b8faedb7f9f697b0c599084e.gif" alt="restart; with(inttrans); with(SumTools); i := 3; network := sqrt(2*p)*(s-p)^(i-1)/(s+p)^i; ztrans(network, s, z)" width="576" height="95" align="middle"&gt;&lt;/p&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -52;" src="/view.aspx?sf=143164/453331/fdb5e4f759d8db1fa4a0788340b7cfda.gif" alt="2^(1/2)*p^(1/2)*(LerchPhi(1/z, 1, p)-2*p*LerchPhi(1/z, 2, p)+2*p^2*LerchPhi(1/z, 3, p)-2*p*(LerchPhi(1/z, 2, p)-p*LerchPhi(1/z, 3, p)))" width="546" height="78" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(1)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=143164/453331/f0d31f55702a356c93b6c68f8c5f6dd9.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Compare with the case i:= 7 and the general case&lt;/span&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -78;" src="/view.aspx?sf=143164/453331/63d9063379aacf00f245f6d38cb4105e.gif" alt="restart; with(inttrans); with(SumTools); network := sqrt(2*p)*(s-p)^(i-1)/(s+p)^i; `assuming`([ztrans(network, s, z)], [s &amp;gt; 0, p &amp;gt; 0, p &amp;gt; s])" width="576" height="95" align="middle"&gt;&lt;/p&gt;
&lt;table&gt;
&lt;tbody&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -20;" src="/view.aspx?sf=143164/453331/53ec5993eae255c3ba4ab4ff61658be5.gif" alt="-2^(1/2)*p^(1/2)*(cos(Pi*i)+I*sin(Pi*i))*ztrans((p-s)^i/((s+p)^i*(p-s)), s, z)" width="402" height="50"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(2)&lt;/td&gt;
&lt;/tr&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=143164/453331/c81335f51184bf109ee3ec18ad737c36.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;
&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=143164/453331/ztrans.mw"&gt;Download ztrans.mw&lt;/a&gt;&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;form name="worksheet_form"&gt;
&lt;table style="width: 576px;" align="center"&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -78;" src="/view.aspx?sf=143164/453331/9917c1e2b8faedb7f9f697b0c599084e.gif" alt="restart; with(inttrans); with(SumTools); i := 3; network := sqrt(2*p)*(s-p)^(i-1)/(s+p)^i; ztrans(network, s, z)" width="576" height="95" align="middle"&gt;&lt;/p&gt;
&lt;table&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -52;" src="/view.aspx?sf=143164/453331/fdb5e4f759d8db1fa4a0788340b7cfda.gif" alt="2^(1/2)*p^(1/2)*(LerchPhi(1/z, 1, p)-2*p*LerchPhi(1/z, 2, p)+2*p^2*LerchPhi(1/z, 3, p)-2*p*(LerchPhi(1/z, 2, p)-p*LerchPhi(1/z, 3, p)))" width="546" height="78" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(1)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=143164/453331/f0d31f55702a356c93b6c68f8c5f6dd9.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Compare with the case i:= 7 and the general case&lt;/span&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -78;" src="/view.aspx?sf=143164/453331/63d9063379aacf00f245f6d38cb4105e.gif" alt="restart; with(inttrans); with(SumTools); network := sqrt(2*p)*(s-p)^(i-1)/(s+p)^i; `assuming`([ztrans(network, s, z)], [s &amp;gt; 0, p &amp;gt; 0, p &amp;gt; s])" width="576" height="95" align="middle"&gt;&lt;/p&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -20;" src="/view.aspx?sf=143164/453331/53ec5993eae255c3ba4ab4ff61658be5.gif" alt="-2^(1/2)*p^(1/2)*(cos(Pi*i)+I*sin(Pi*i))*ztrans((p-s)^i/((s+p)^i*(p-s)), s, z)" width="402" height="50"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(2)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=143164/453331/c81335f51184bf109ee3ec18ad737c36.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;
&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=143164/453331/ztrans.mw"&gt;Download ztrans.mw&lt;/a&gt;&lt;/p&gt;</description>
      <guid>143164</guid>
      <pubDate>Wed, 06 Feb 2013 18:48:42 Z</pubDate>
      <itunes:author>Markiyan Hirnyk</itunes:author>
      <author>Markiyan Hirnyk</author>
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      <title>the general case result (2) still has ztrans,</title>
      <link>http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive?ref=Feed:MaplePrimes:error recursive equation but it is not recursive:Comments#comment143167</link>
      <itunes:summary>&lt;p&gt;the general case result (2) still has ztrans, it should be a simple rational function&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;the general case result (2) still has ztrans, it should be a simple rational function&lt;/p&gt;</description>
      <guid>143167</guid>
      <pubDate>Wed, 06 Feb 2013 19:05:03 Z</pubDate>
      <itunes:author>williamov</itunes:author>
      <author>williamov</author>
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      <title>Arguments?</title>
      <link>http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive?ref=Feed:MaplePrimes:error recursive equation but it is not recursive:Comments#comment143174</link>
      <itunes:summary>&lt;p&gt;&lt;a href="http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive#comment143167"&gt;@williamov&lt;/a&gt; Why do you think so?&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;&lt;a href="http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive#comment143167"&gt;@williamov&lt;/a&gt; Why do you think so?&lt;/p&gt;</description>
      <guid>143174</guid>
      <pubDate>Wed, 06 Feb 2013 20:08:23 Z</pubDate>
      <itunes:author>Markiyan Hirnyk</itunes:author>
      <author>Markiyan Hirnyk</author>
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      <title>i think this because chapter 3 page 86
3.2.1</title>
      <link>http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive?ref=Feed:MaplePrimes:error recursive equation but it is not recursive:Comments#comment143225</link>
      <itunes:summary>&lt;p&gt;i think this because chapter 3 page 86&lt;/p&gt;
&lt;p&gt;3.2.1 said&amp;nbsp; z-transform of this network can be written as&lt;/p&gt;
&lt;p&gt;rational function (3.1)&lt;/p&gt;
&lt;p&gt;can be downloaded here&lt;/p&gt;
&lt;p&gt;http://ishare.iask.sina.com.cn/f/33653381.html&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;i think this because chapter 3 page 86&lt;/p&gt;
&lt;p&gt;3.2.1 said&amp;nbsp; z-transform of this network can be written as&lt;/p&gt;
&lt;p&gt;rational function (3.1)&lt;/p&gt;
&lt;p&gt;can be downloaded here&lt;/p&gt;
&lt;p&gt;http://ishare.iask.sina.com.cn/f/33653381.html&lt;/p&gt;</description>
      <guid>143225</guid>
      <pubDate>Thu, 07 Feb 2013 17:30:30 Z</pubDate>
      <itunes:author>williamov</itunes:author>
      <author>williamov</author>
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      <title>I can download nothing from that link</title>
      <link>http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive?ref=Feed:MaplePrimes:error recursive equation but it is not recursive:Comments#comment143241</link>
      <itunes:summary>&lt;p&gt;&lt;a href="http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive#comment143225"&gt;@williamov&lt;/a&gt; Can you kindly present the e-paper you referred to in MaplePrimes as an attached file?&lt;/p&gt;
&lt;p&gt;PS. If &lt;span class="mainBody document"&gt;ztrans(network, s, z);&lt;/span&gt; were a rational function of z in the general case, then it also were so for concrete i.&lt;/p&gt;
&lt;p&gt;However, &lt;span class="mainBody document"&gt;ztrans(network, s, z);&lt;/span&gt; is not a rational function of z if i=3 (see my above answer). &lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;&lt;a href="http://www.mapleprimes.com/questions/143160-Error-Recursive-Equation-But-It-Is-Not-Recursive#comment143225"&gt;@williamov&lt;/a&gt; Can you kindly present the e-paper you referred to in MaplePrimes as an attached file?&lt;/p&gt;
&lt;p&gt;PS. If &lt;span class="mainBody document"&gt;ztrans(network, s, z);&lt;/span&gt; were a rational function of z in the general case, then it also were so for concrete i.&lt;/p&gt;
&lt;p&gt;However, &lt;span class="mainBody document"&gt;ztrans(network, s, z);&lt;/span&gt; is not a rational function of z if i=3 (see my above answer). &lt;/p&gt;</description>
      <guid>143241</guid>
      <pubDate>Thu, 07 Feb 2013 23:00:38 Z</pubDate>
      <itunes:author>Markiyan Hirnyk</itunes:author>
      <author>Markiyan Hirnyk</author>
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