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TeX (original user input):

X(t) = \sum_{n=-\infty}^\infty  e^{2\pi i nt / T} X_n

TeX (checked):

X(t)=\sum _{n=-\infty }^{\infty }e^{2\pi int/T}X_{n}

LaTeXML (experimental; uses MathML) rendering

MathML (6.705 KB / 1.193 KB) :

X ( t ) = n = - e 2 π i n t / T X n 𝑋 𝑡 superscript subscript 𝑛 superscript 𝑒 2 𝜋 𝑖 𝑛 𝑡 𝑇 subscript 𝑋 𝑛 {\displaystyle X(t)=\sum_{{n=-\infty}}^{\infty}e^{{2\pi int/T}}X_{n}}
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SVG (11.594 KB / 4.232 KB) :

upper X times left-parenthesis t right-parenthesis equals sigma-summation Underscript n equals negative normal infinity Overscript normal infinity Endscripts e Superscript 2 times pi times i times n times t slash upper T Baseline times upper X Subscript n

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: X*(t)= sum((e)^(2*pi*i*n*t/ T)* X[n], n = - infinity..infinity)

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


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



Translation to Mathematica

In Mathematica: X*(t)= Sum[(e)^(2*\[Pi]*i*n*t/ T)* Subscript[X, n], {n, - Infinity, Infinity}]

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


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



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