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Display information for equation id:math.232459.1 on revision:232459

* Page found: Trigonometric polynomial (eq math.232459.1)

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Hash: 6bd41df23809f5ea29926c76a82834b7

TeX (original user input):

T(x) = \sum_{n=-N}^N c_n \mathrm{e}^{\mathrm{i}nx} \qquad (x \in \mathbf{R}).

TeX (checked):

T(x)=\sum _{n=-N}^{N}c_{n}\mathrm {e} ^{\mathrm {i} nx}\qquad (x\in \mathbf {R} ).

LaTeXML (experimental; uses MathML) rendering

MathML (6.242 KB / 1.254 KB) :

T ( x ) = n = - N N c n e i n x    ( x 𝐑 ) . fragments T fragments ( x ) superscript subscript 𝑛 𝑁 𝑁 subscript 𝑐 𝑛 superscript e i 𝑛 𝑥 italic-   fragments ( x R ) . {\displaystyle T(x)=\sum_{{n=-N}}^{N}c_{n}{\mathrm{e}}^{{{\mathrm{i}}nx}}% \qquad(x\in{\mathbf{R}}).}
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SVG (10.649 KB / 3.927 KB) :

upper T left-parenthesis x right-parenthesis equals sigma-summation Underscript n equals negative upper N Overscript upper N Endscripts c Subscript n Baseline normal e Superscript normal i times n times x Baseline italic left-parenthesis x element-of bold upper R right-parenthesis period

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

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SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple: T*(x)= sum(c[n]*(e)^(i*n*x)*(x in R), n = - N..N)

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: T*(x)= Sum[Subscript[c, n]*(e)^(i*n*x)*(x \[Element]*R), {n, - N, N}]

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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