<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0"><channel><title><![CDATA[Kugelintegral transformieren]]></title><description><![CDATA[<p>Hallo zusammen,</p>
<p>ich würde gerne ein Integral der Form</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mo>∫</mo><mrow><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><mi>x</mi><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><mo>&lt;</mo><mn>1</mn></mrow></msub><msub><mo>∫</mo><mrow><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><mi>y</mi><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><mo>&lt;</mo><mn>1</mn></mrow></msub><mi>f</mi><mo>(</mo><mi mathvariant="normal">∣</mi><mi>x</mi><mo>−</mo><mi>y</mi><mi mathvariant="normal">∣</mi><mo>)</mo><mspace width="0.277778em"></mspace><msup><mrow><mi mathvariant="normal">d</mi></mrow><mi>n</mi></msup><mi>x</mi><mspace width="0.277778em"></mspace><msup><mrow><mi mathvariant="normal">d</mi></mrow><mi>n</mi></msup><mi>y</mi></mrow><annotation encoding="application/x-tex">\int_{||x|| &lt; 1} \int_{||y|| &lt; 1} f(|x-y|) \; \mathrm{d}^n x \; \mathrm{d}^n y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.805em;"></span><span class="strut bottom" style="height:1.3361200000000002em;vertical-align:-0.53112em;"></span><span class="base textstyle uncramped"><span class="mop"><span class="op-symbol small-op mop" style="margin-right:0.19445em;top:-0.0005599999999999772em;">∫</span><span class="vlist"><span style="top:0.35612000000000005em;margin-right:0.05em;margin-left:-0.19445em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathrm">∣</span><span class="mord mathrm">∣</span><span class="mord mathit">x</span><span class="mord mathrm">∣</span><span class="mord mathrm">∣</span><span class="mrel">&lt;</span><span class="mord mathrm">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mop"><span class="op-symbol small-op mop" style="margin-right:0.19445em;top:-0.0005599999999999772em;">∫</span><span class="vlist"><span style="top:0.35612000000000005em;margin-right:0.05em;margin-left:-0.19445em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathrm">∣</span><span class="mord mathrm">∣</span><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="mord mathrm">∣</span><span class="mord mathrm">∣</span><span class="mrel">&lt;</span><span class="mord mathrm">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathrm">∣</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="mord mathrm">∣</span><span class="mclose">)</span><span class="mord mspace thickspace"></span><span class=""><span class="mord textstyle uncramped"><span class="mord mathrm">d</span></span><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathit">n</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mord mathit">x</span><span class="mord mspace thickspace"></span><span class=""><span class="mord textstyle uncramped"><span class="mord mathrm">d</span></span><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathit">n</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mord mathit" style="margin-right:0.03588em;">y</span></span></span></span></p>
<p>als</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mo>∫</mo><mn>0</mn><mn>2</mn></msubsup><mi>g</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mspace width="0.277778em"></mspace><mrow><mi mathvariant="normal">d</mi></mrow><mi>z</mi></mrow><annotation encoding="application/x-tex">\int_0^2 g(z) f(z) \; \mathrm{d}z</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.870108em;"></span><span class="strut bottom" style="height:1.2262279999999999em;vertical-align:-0.35612em;"></span><span class="base textstyle uncramped"><span class="mop"><span class="op-symbol small-op mop" style="margin-right:0.19445em;top:-0.0005599999999999772em;">∫</span><span class="vlist"><span style="top:0.35612em;margin-left:-0.19445em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord mathrm">0</span></span></span><span style="top:-0.41900000000000004em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathrm">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mord mathit" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.04398em;">z</span><span class="mclose">)</span><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.04398em;">z</span><span class="mclose">)</span><span class="mord mspace thickspace"></span><span class="mord textstyle uncramped"><span class="mord mathrm">d</span></span><span class="mord mathit" style="margin-right:0.04398em;">z</span></span></span></span></p>
<p>schreiben.</p>
<p>Wie berechnet man g(z)?</p>
]]></description><link>https://www.c-plusplus.net/forum/topic/343513/kugelintegral-transformieren</link><generator>RSS for Node</generator><lastBuildDate>Mon, 14 Sep 2026 23:44:28 GMT</lastBuildDate><atom:link href="https://www.c-plusplus.net/forum/topic/343513.rss" rel="self" type="application/rss+xml"/><pubDate>Wed, 28 Jun 2017 19:11:28 GMT</pubDate><ttl>60</ttl><item><title><![CDATA[Reply to Kugelintegral transformieren on Wed, 28 Jun 2017 19:11:28 GMT]]></title><description><![CDATA[<p>Hallo zusammen,</p>
<p>ich würde gerne ein Integral der Form</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mo>∫</mo><mrow><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><mi>x</mi><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><mo>&lt;</mo><mn>1</mn></mrow></msub><msub><mo>∫</mo><mrow><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><mi>y</mi><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><mo>&lt;</mo><mn>1</mn></mrow></msub><mi>f</mi><mo>(</mo><mi mathvariant="normal">∣</mi><mi>x</mi><mo>−</mo><mi>y</mi><mi mathvariant="normal">∣</mi><mo>)</mo><mspace width="0.277778em"></mspace><msup><mrow><mi mathvariant="normal">d</mi></mrow><mi>n</mi></msup><mi>x</mi><mspace width="0.277778em"></mspace><msup><mrow><mi mathvariant="normal">d</mi></mrow><mi>n</mi></msup><mi>y</mi></mrow><annotation encoding="application/x-tex">\int_{||x|| &lt; 1} \int_{||y|| &lt; 1} f(|x-y|) \; \mathrm{d}^n x \; \mathrm{d}^n y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.805em;"></span><span class="strut bottom" style="height:1.3361200000000002em;vertical-align:-0.53112em;"></span><span class="base textstyle uncramped"><span class="mop"><span class="op-symbol small-op mop" style="margin-right:0.19445em;top:-0.0005599999999999772em;">∫</span><span class="vlist"><span style="top:0.35612000000000005em;margin-right:0.05em;margin-left:-0.19445em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathrm">∣</span><span class="mord mathrm">∣</span><span class="mord mathit">x</span><span class="mord mathrm">∣</span><span class="mord mathrm">∣</span><span class="mrel">&lt;</span><span class="mord mathrm">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mop"><span class="op-symbol small-op mop" style="margin-right:0.19445em;top:-0.0005599999999999772em;">∫</span><span class="vlist"><span style="top:0.35612000000000005em;margin-right:0.05em;margin-left:-0.19445em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathrm">∣</span><span class="mord mathrm">∣</span><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="mord mathrm">∣</span><span class="mord mathrm">∣</span><span class="mrel">&lt;</span><span class="mord mathrm">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathrm">∣</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="mord mathrm">∣</span><span class="mclose">)</span><span class="mord mspace thickspace"></span><span class=""><span class="mord textstyle uncramped"><span class="mord mathrm">d</span></span><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathit">n</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mord mathit">x</span><span class="mord mspace thickspace"></span><span class=""><span class="mord textstyle uncramped"><span class="mord mathrm">d</span></span><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathit">n</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mord mathit" style="margin-right:0.03588em;">y</span></span></span></span></p>
<p>als</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mo>∫</mo><mn>0</mn><mn>2</mn></msubsup><mi>g</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mspace width="0.277778em"></mspace><mrow><mi mathvariant="normal">d</mi></mrow><mi>z</mi></mrow><annotation encoding="application/x-tex">\int_0^2 g(z) f(z) \; \mathrm{d}z</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.870108em;"></span><span class="strut bottom" style="height:1.2262279999999999em;vertical-align:-0.35612em;"></span><span class="base textstyle uncramped"><span class="mop"><span class="op-symbol small-op mop" style="margin-right:0.19445em;top:-0.0005599999999999772em;">∫</span><span class="vlist"><span style="top:0.35612em;margin-left:-0.19445em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord mathrm">0</span></span></span><span style="top:-0.41900000000000004em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathrm">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mord mathit" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.04398em;">z</span><span class="mclose">)</span><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.04398em;">z</span><span class="mclose">)</span><span class="mord mspace thickspace"></span><span class="mord textstyle uncramped"><span class="mord mathrm">d</span></span><span class="mord mathit" style="margin-right:0.04398em;">z</span></span></span></span></p>
<p>schreiben.</p>
<p>Wie berechnet man g(z)?</p>
]]></description><link>https://www.c-plusplus.net/forum/post/2533731</link><guid isPermaLink="true">https://www.c-plusplus.net/forum/post/2533731</guid><dc:creator><![CDATA[C14]]></dc:creator><pubDate>Wed, 28 Jun 2017 19:11:28 GMT</pubDate></item><item><title><![CDATA[Reply to Kugelintegral transformieren on Wed, 28 Jun 2017 23:29:46 GMT]]></title><description><![CDATA[<p><a href="https://de.wikipedia.org/wiki/Polarkoordinaten" rel="nofollow">https://de.wikipedia.org/wiki/Polarkoordinaten</a></p>
]]></description><link>https://www.c-plusplus.net/forum/post/2533746</link><guid isPermaLink="true">https://www.c-plusplus.net/forum/post/2533746</guid><dc:creator><![CDATA[Kenner der Integrale]]></dc:creator><pubDate>Wed, 28 Jun 2017 23:29:46 GMT</pubDate></item></channel></rss>