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Display information for equation id:math.232459.0 on revision:232459

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Hash: 57c450726eb56ce0856937ede817fc5a

TeX (original user input):

T(x) = a_0 + \sum_{n=1}^N a_n \cos (nx) + \mathrm{i}\sum_{n=1}^N b_n \sin(nx) \qquad (x \in \mathbf{R})

TeX (checked):

T(x)=a_{0}+\sum _{n=1}^{N}a_{n}\cos(nx)+\mathrm {i} \sum _{n=1}^{N}b_{n}\sin(nx)\qquad (x\in \mathbf {R} )

LaTeXML (experimental; uses MathML) rendering

MathML (9.38 KB / 1.561 KB) :

T ( x ) = a 0 + n = 1 N a n cos ( n x ) + i n = 1 N b n sin ( n x )    ( x 𝐑 ) fragments T fragments ( x ) subscript 𝑎 0 superscript subscript 𝑛 1 𝑁 subscript 𝑎 𝑛 fragments ( n x ) i superscript subscript 𝑛 1 𝑁 subscript 𝑏 𝑛 fragments ( n x ) italic-   fragments ( x R ) {\displaystyle T(x)=a_{0}+\sum_{{n=1}}^{N}a_{n}\cos(nx)+{\mathrm{i}}\sum_{{n=1% }}^{N}b_{n}\sin(nx)\qquad(x\in{\mathbf{R}})}
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SVG (15.838 KB / 5.474 KB) :

upper T left-parenthesis x right-parenthesis equals a 0 plus sigma-summation Underscript n equals 1 Overscript upper N Endscripts a Subscript n Baseline cosine left-parenthesis n x right-parenthesis plus normal i sigma-summation Underscript n equals 1 Overscript upper N Endscripts b Subscript n Baseline sine left-parenthesis n x right-parenthesis italic left-parenthesis x element-of bold upper R right-parenthesis

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: T*(x)= a[0]+ sum(a[n]*cos(n*x), n = 1..N)+ i*sum(b[n]*sin((n*x)*)*(x in R), n = 1..N)

Information about the conversion process:

\cos: Cosine; Example: \cos@@{z}

Will be translated to: cos($0)

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E2

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos


\sin: Sine; Example: \sin@@{z}

Will be translated to: sin($0)

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E1

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin


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


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


Translation to Mathematica

In Mathematica: T*(x)= Subscript[a, 0]+ Sum[Subscript[a, n]*Cos[n*x], {n, 1, N}]+ i*Sum[Subscript[b, n]*Sin[(n*x)*]*(x \[Element]*R), {n, 1, N}]

Information about the conversion process:

\cos: Cosine; Example: \cos@@{z}

Will be translated to: Cos[$0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E2

Mathematica: https://reference.wolfram.com/language/ref/Cos.html


\sin: Sine; Example: \sin@@{z}

Will be translated to: Sin[$0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E1

Mathematica: https://reference.wolfram.com/language/ref/Sin.html


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


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


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