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Display information for equation id:math.219374.43 on revision:219374

* Page found: Euler's formula (eq math.219374.43)

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Occurrences on the following pages:

Hash: b8a74bd4a57bf1d1068d3cb240498581

TeX (original user input):

i e ^{ix}

TeX (checked):

ie^{ix}

LaTeXML (experimental; uses MathML) rendering

MathML (1.681 KB / 488 B) :

i e i x 𝑖 superscript 𝑒 𝑖 𝑥 {\displaystyle ie^{{ix}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle ie^{{ix}}}" display="inline">
  <semantics id="p1.1.m1.1a">
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      <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">i</mi>
      <mo id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml"></mo>
      <msup id="p1.1.m1.1.4.2" xref="p1.1.m1.1.4.2.cmml">
        <mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">e</mi>
        <mrow id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">
          <mi id="p1.1.m1.1.3.1.1" xref="p1.1.m1.1.3.1.1.cmml">i</mi>
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          <mi id="p1.1.m1.1.3.1.2" xref="p1.1.m1.1.3.1.2.cmml">x</mi>
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        <times id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1"/>
        <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑖</ci>
        <apply id="p1.1.m1.1.4.2.cmml" xref="p1.1.m1.1.4.2">
          <csymbol cd="ambiguous" id="p1.1.m1.1.4.2.1.cmml" xref="p1.1.m1.1.4.2">superscript</csymbol>
          <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">𝑒</ci>
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            <ci id="p1.1.m1.1.3.1.2.cmml" xref="p1.1.m1.1.3.1.2">𝑥</ci>
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    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle ie^{{ix}}}</annotation>
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</math>

SVG (2.96 KB / 1.316 KB) :

i times e Superscript i times x

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

MathML (0 B / 8 B) :

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SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple: i*(e)^(i*x)

Information about the conversion process:

I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

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

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


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


i: the imaginary unit == the principal square root of -1 was translated to: i


Translation to Mathematica

In Mathematica: i*(e)^(i*x)

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


I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

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

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


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

i: the imaginary unit == the principal square root of -1 was translated to: i


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