Jump to navigation Jump to search

General

Display information for equation id:math.227562.8 on revision:227562

* Page found: Fredholm operator (eq math.227562.8)

(force rerendering)

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

Occurrences on the following pages:

Hash: 9a1e5046d03a1abbd1d02b6e2ff58c35

TeX (original user input):

S^*(e_0) = 0, \ \ S^*(e_n) = e_{n-1}, \quad n \ge 1. \,

TeX (checked):

S^{*}(e_{0})=0,\ \ S^{*}(e_{n})=e_{n-1},\quad n\geq 1.\,

LaTeXML (experimental; uses MathML) rendering

MathML (7.354 KB / 1.199 KB) :

S * ( e 0 ) = 0 , S * ( e n ) = e n - 1 , n 1 . formulae-sequence superscript 𝑆 subscript 𝑒 0 0 formulae-sequence superscript 𝑆 subscript 𝑒 𝑛 subscript 𝑒 𝑛 1 𝑛 1 {\displaystyle S^{*}(e_{0})=0,\ \ S^{*}(e_{n})=e_{{n-1}},\quad n\geq 1.\,}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle S^{*}(e_{0})=0,\ \ S^{*}(e_{n})=e_{{n-1}},\quad n\geq 1.\,}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.28">
      <mrow id="p1.1.m1.1.28.2" xref="p1.1.m1.1.28.2.1.cmml">
        <mrow id="p1.1.m1.1.28.2.2" xref="p1.1.m1.1.28.2.2.cmml">
          <mrow id="p1.1.m1.1.28.2.2.1" xref="p1.1.m1.1.28.2.2.1.cmml">
            <msup id="p1.1.m1.1.28.2.2.1.2" xref="p1.1.m1.1.28.2.2.1.2.cmml">
              <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">S</mi>
              <mo id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">*</mo>
            </msup>
            <mo id="p1.1.m1.1.28.2.2.1.1" xref="p1.1.m1.1.28.2.2.1.1.cmml"></mo>
            <mrow id="p1.1.m1.1.28.2.2.1.3" xref="p1.1.m1.1.28.2.2.1.3.2.cmml">
              <mo stretchy="false" id="p1.1.m1.1.3" xref="p1.1.m1.1.28.2.2.1.3.2.cmml">(</mo>
              <msub id="p1.1.m1.1.28.2.2.1.3.2" xref="p1.1.m1.1.28.2.2.1.3.2.cmml">
                <mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">e</mi>
                <mn id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">0</mn>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.28.2.2.1.3.2.cmml">)</mo>
            </mrow>
          </mrow>
          <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
          <mn id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">0</mn>
        </mrow>
        <mo rspace="12.5pt" id="p1.1.m1.1.9" xref="p1.1.m1.1.28.2.1a.cmml">,</mo>
        <mrow id="p1.1.m1.1.28.2.3" xref="p1.1.m1.1.28.2.3.1.cmml">
          <mrow id="p1.1.m1.1.28.2.3.2" xref="p1.1.m1.1.28.2.3.2.cmml">
            <mrow id="p1.1.m1.1.28.2.3.2.1" xref="p1.1.m1.1.28.2.3.2.1.cmml">
              <msup id="p1.1.m1.1.28.2.3.2.1.2" xref="p1.1.m1.1.28.2.3.2.1.2.cmml">
                <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">S</mi>
                <mo id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">*</mo>
              </msup>
              <mo id="p1.1.m1.1.28.2.3.2.1.1" xref="p1.1.m1.1.28.2.3.2.1.1.cmml"></mo>
              <mrow id="p1.1.m1.1.28.2.3.2.1.3" xref="p1.1.m1.1.28.2.3.2.1.3.2.cmml">
                <mo stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.28.2.3.2.1.3.2.cmml">(</mo>
                <msub id="p1.1.m1.1.28.2.3.2.1.3.2" xref="p1.1.m1.1.28.2.3.2.1.3.2.cmml">
                  <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">e</mi>
                  <mi id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">n</mi>
                </msub>
                <mo stretchy="false" id="p1.1.m1.1.17" xref="p1.1.m1.1.28.2.3.2.1.3.2.cmml">)</mo>
              </mrow>
            </mrow>
            <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">=</mo>
            <msub id="p1.1.m1.1.28.2.3.2.2" xref="p1.1.m1.1.28.2.3.2.2.cmml">
              <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">e</mi>
              <mrow id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">
                <mi id="p1.1.m1.1.20.1.1" xref="p1.1.m1.1.20.1.1.cmml">n</mi>
                <mo id="p1.1.m1.1.20.1.2" xref="p1.1.m1.1.20.1.2.cmml">-</mo>
                <mn id="p1.1.m1.1.20.1.3" xref="p1.1.m1.1.20.1.3.cmml">1</mn>
              </mrow>
            </msub>
          </mrow>
          <mo rspace="12.5pt" id="p1.1.m1.1.21" xref="p1.1.m1.1.28.2.3.1a.cmml">,</mo>
          <mrow id="p1.1.m1.1.28.2.3.3" xref="p1.1.m1.1.28.2.3.3.cmml">
            <mi id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">n</mi>
            <mo id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml"></mo>
            <mn id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">1</mn>
          </mrow>
        </mrow>
      </mrow>
      <mo rspace="4.2pt" id="p1.1.m1.1.26">.</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.28.2.1.cmml" xref="p1.1.m1.1.28.2">
        <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.1a.cmml" xref="p1.1.m1.1.9">formulae-sequence</csymbol>
        <apply id="p1.1.m1.1.28.2.2.cmml" xref="p1.1.m1.1.28.2.2">
          <eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
          <apply id="p1.1.m1.1.28.2.2.1.cmml" xref="p1.1.m1.1.28.2.2.1">
            <times id="p1.1.m1.1.28.2.2.1.1.cmml" xref="p1.1.m1.1.28.2.2.1.1"/>
            <apply id="p1.1.m1.1.28.2.2.1.2.cmml" xref="p1.1.m1.1.28.2.2.1.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.1.2.1.cmml" xref="p1.1.m1.1.28.2.2.1.2">superscript</csymbol>
              <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑆</ci>
              <times id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1"/>
            </apply>
            <apply id="p1.1.m1.1.28.2.2.1.3.2.cmml" xref="p1.1.m1.1.28.2.2.1.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.1.3.2.1.cmml" xref="p1.1.m1.1.28.2.2.1.3">subscript</csymbol>
              <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝑒</ci>
              <cn type="integer" id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">0</cn>
            </apply>
          </apply>
          <cn type="integer" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">0</cn>
        </apply>
        <apply id="p1.1.m1.1.28.2.3.1.cmml" xref="p1.1.m1.1.28.2.3">
          <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.3.1a.cmml" xref="p1.1.m1.1.21">formulae-sequence</csymbol>
          <apply id="p1.1.m1.1.28.2.3.2.cmml" xref="p1.1.m1.1.28.2.3.2">
            <eq id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18"/>
            <apply id="p1.1.m1.1.28.2.3.2.1.cmml" xref="p1.1.m1.1.28.2.3.2.1">
              <times id="p1.1.m1.1.28.2.3.2.1.1.cmml" xref="p1.1.m1.1.28.2.3.2.1.1"/>
              <apply id="p1.1.m1.1.28.2.3.2.1.2.cmml" xref="p1.1.m1.1.28.2.3.2.1.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.3.2.1.2.1.cmml" xref="p1.1.m1.1.28.2.3.2.1.2">superscript</csymbol>
                <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝑆</ci>
                <times id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1"/>
              </apply>
              <apply id="p1.1.m1.1.28.2.3.2.1.3.2.cmml" xref="p1.1.m1.1.28.2.3.2.1.3">
                <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.3.2.1.3.2.1.cmml" xref="p1.1.m1.1.28.2.3.2.1.3">subscript</csymbol>
                <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">𝑒</ci>
                <ci id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">𝑛</ci>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.28.2.3.2.2.cmml" xref="p1.1.m1.1.28.2.3.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.3.2.2.1.cmml" xref="p1.1.m1.1.28.2.3.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">𝑒</ci>
              <apply id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">
                <minus id="p1.1.m1.1.20.1.2.cmml" xref="p1.1.m1.1.20.1.2"/>
                <ci id="p1.1.m1.1.20.1.1.cmml" xref="p1.1.m1.1.20.1.1">𝑛</ci>
                <cn type="integer" id="p1.1.m1.1.20.1.3.cmml" xref="p1.1.m1.1.20.1.3">1</cn>
              </apply>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.28.2.3.3.cmml" xref="p1.1.m1.1.28.2.3.3">
            <geq id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24"/>
            <ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">𝑛</ci>
            <cn type="integer" id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">1</cn>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle S^{*}(e_{0})=0,\ \ S^{*}(e_{n})=e_{{n-1}},\quad n\geq 1.\,}</annotation>
  </semantics>
</math>

SVG (9.73 KB / 3.133 KB) :

upper S Superscript asterisk Baseline times left-parenthesis e 0 right-parenthesis equals 0 comma upper S Superscript asterisk Baseline times left-parenthesis e Subscript n Baseline right-parenthesis equals e Subscript n minus 1 Baseline comma n greater-than-or-equal-to 1 period

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: (S)^(*)*(e[0])= 0 , (S)^(*)*(e[n])= e[n - 1], n >= 1

Information about the conversion process:

e: the mathematical constant e == Napier's constant == 2.71828182845... was translated to: e

exp(1): You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].

We keep it like it is! But you should know that Maple uses exp(1) for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \expe



Translation to Mathematica

In Mathematica: (S)^(*)*(Subscript[e, 0])= 0 , (S)^(*)*(Subscript[e, n])= Subscript[e, n - 1], n >= 1

Information about the conversion process:

E: You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].

We keep it like it is! But you should know that Mathematica uses E for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \expe


e: the mathematical constant e == Napier's constant == 2.71828182845... was translated to: e


Similar pages

Calculated based on the variables occurring on the entire Fredholm operator page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results