Jump to navigation Jump to search

General

Display information for equation id:math.254408.8 on revision:254408

* Page found: Marsaglia polar method (eq math.254408.8)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: 6435fec3db0dab5b9f92c64120a08d3d

TeX (original user input):

\sqrt{-2\ln(u_1)};

TeX (checked):

{\sqrt {-2\ln(u_{1})}};

LaTeXML (experimental; uses MathML) rendering

MathML (2.774 KB / 648 B) :

- 2 ln ( u 1 ) ; 2 subscript u 1 {\displaystyle{\sqrt{-2\ln(u_{1})}};}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\sqrt{-2\ln(u_{1})}};}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
      <msqrt id="p1.1.m1.1.1a" xref="p1.1.m1.1.1.cmml">
        <mrow id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">
          <mo id="p1.1.m1.1.1.2.1" xref="p1.1.m1.1.1.2.1.cmml">-</mo>
          <mrow id="p1.1.m1.1.1.2.8" xref="p1.1.m1.1.1.2.8.cmml">
            <mn id="p1.1.m1.1.1.2.2" xref="p1.1.m1.1.1.2.2.cmml">2</mn>
            <mo id="p1.1.m1.1.1.2.8.1" xref="p1.1.m1.1.1.2.8.1.cmml"></mo>
            <mrow id="p1.1.m1.1.1.2.8.2.2" xref="p1.1.m1.1.1.2.8.2.1.cmml">
              <mi id="p1.1.m1.1.1.2.3" xref="p1.1.m1.1.1.2.3.cmml">ln</mi>
              <mo id="p1.1.m1.1.1.2.8.2.2a" xref="p1.1.m1.1.1.2.8.2.1.cmml"></mo>
              <mrow id="p1.1.m1.1.1.2.8.2" xref="p1.1.m1.1.1.2.8.2.1.cmml">
                <mo stretchy="false" id="p1.1.m1.1.1.2.4" xref="p1.1.m1.1.1.2.8.2.1.cmml">(</mo>
                <msub id="p1.1.m1.1.1.2.8.2.2.1" xref="p1.1.m1.1.1.2.8.2.1.cmml">
                  <mi id="p1.1.m1.1.1.2.5" xref="p1.1.m1.1.1.2.5.cmml">u</mi>
                  <mn id="p1.1.m1.1.1.2.6.1" xref="p1.1.m1.1.1.2.6.1.cmml">1</mn>
                </msub>
                <mo stretchy="false" id="p1.1.m1.1.1.2.7" xref="p1.1.m1.1.1.2.8.2.1.cmml">)</mo>
              </mrow>
            </mrow>
          </mrow>
        </mrow>
      </msqrt>
      <mo id="p1.1.m1.1.1b" xref="p1.1.m1.1.1.cmml">;</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
        <root id="p1.1.m1.1.1a.cmml" xref="p1.1.m1.1.1"/>
        <apply id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">
          <minus id="p1.1.m1.1.1.2.1.cmml" xref="p1.1.m1.1.1.2.1"/>
          <apply id="p1.1.m1.1.1.2.8.cmml" xref="p1.1.m1.1.1.2.8">
            <times id="p1.1.m1.1.1.2.8.1.cmml" xref="p1.1.m1.1.1.2.8.1"/>
            <cn type="integer" id="p1.1.m1.1.1.2.2.cmml" xref="p1.1.m1.1.1.2.2">2</cn>
            <apply id="p1.1.m1.1.1.2.8.2.1.cmml" xref="p1.1.m1.1.1.2.8.2.2">
              <ln id="p1.1.m1.1.1.2.3.cmml" xref="p1.1.m1.1.1.2.3"/>
              <apply id="p1.1.m1.1.1.2.8.2.2.1.cmml" xref="p1.1.m1.1.1.2.8.2.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.1.2.8.2.2.1.1.cmml">subscript</csymbol>
                <ci id="p1.1.m1.1.1.2.5.cmml" xref="p1.1.m1.1.1.2.5">u</ci>
                <cn type="integer" id="p1.1.m1.1.1.2.6.1.cmml" xref="p1.1.m1.1.1.2.6.1">1</cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\sqrt{-2\ln(u_{1})}};}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (6.09 KB / 2.472 KB) :

StartRoot minus 2 times ln left-parenthesis u 1 right-parenthesis EndRoot semicolon

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple: sqrt(- 2*ln(u[1]))

Information about the conversion process:

\ln: Natural logarithm; Example: \ln@@{z}

Will be translated to: ln($0)

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=ln



Translation to Mathematica

In Mathematica: Sqrt[- 2*Log[Subscript[u, 1]]]

Information about the conversion process:

\ln: Natural logarithm; Example: \ln@@{z}

Will be translated to: Log[$0]

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

Mathematica: https://reference.wolfram.com/language/ref/Log.html



Similar pages

Calculated based on the variables occurring on the entire Marsaglia polar method page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results