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Display information for equation id:math.236684.50 on revision:236684

* Page found: Helmholtz equation (eq math.236684.50)

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Occurrences on the following pages:

Hash: 80c2156dff1d4cf336927fcf24f42ce0

TeX (original user input):

G(x) = \frac{e^{ik|x|}}{4\pi |x|}

TeX (checked):

G(x)={\frac {e^{ik|x|}}{4\pi |x|}}

LaTeXML (experimental; uses MathML) rendering

MathML (4.64 KB / 914 B) :

G ( x ) = e i k | x | 4 π | x | G x superscript e i k x 4 π x {\displaystyle G(x)={\frac{e^{{ik|x|}}}{4\pi|x|}}}
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SVG (8.813 KB / 3.268 KB) :

upper G times left-parenthesis x right-parenthesis equals StartFraction e Superscript i times k times StartAbsoluteValue x EndAbsoluteValue Baseline Over 4 times pi times StartAbsoluteValue x EndAbsoluteValue EndFraction

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

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: G*(x)=((e)^(i*k*abs(x)))/(4*pi*abs(x))

Information about the conversion process:

\pi: Could be the ratio of a circle's circumference to its diameter == Archimedes' constant.

But it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!

Use the DLMF-Macro \cpi to translate \pi as a constant.


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 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: G*(x)=Divide[(e)^(i*k*Abs[x]),4*\[Pi]*Abs[x]]

Information about the conversion process:

\pi: Could be the ratio of a circle's circumference to its diameter == Archimedes' constant.

But it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!

Use the DLMF-Macro \cpi to translate \pi as a constant.


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



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