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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

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${\displaystyle T(x)=a_{0}+\sum_{{n=1}}^{N}a_{n}\cos(nx)+{\mathrm{i}}\sum_{{n=1% }}^{N}b_{n}\sin(nx)\qquad(x\in{\mathbf{R}})}$
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<annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle T(x)=a_{0}+\sum_{{n=1}}^{N}a_{n}\cos(nx)+{\mathrm{i}}\sum_{{n=1%
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[/itex]

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

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)

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

Will be translated to: cos($0) Relevant links to definitions: \sin: Sine; Example: \sin@@{z} Will be translated to: sin($0)

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}]

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

Will be translated to: Cos[$0] Relevant links to definitions: \sin: Sine; Example: \sin@@{z} Will be translated to: Sin[$0]

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

Similar pages

Calculated based on the variables occurring on the entire Trigonometric polynomial page

Identifiers

• ${\displaystyle T}$
• ${\displaystyle x}$
• ${\displaystyle a_{0}}$
• ${\displaystyle n}$
• ${\displaystyle N}$
• ${\displaystyle a_{n}}$
• ${\displaystyle n}$
• ${\displaystyle x}$
• ${\displaystyle {\mathrm {i} }}$
• ${\displaystyle n}$
• ${\displaystyle N}$
• ${\displaystyle b_{n}}$
• ${\displaystyle n}$
• ${\displaystyle x}$
• ${\displaystyle x}$
• ${\displaystyle \mathbf {R} }$

MathML observations

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