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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} )
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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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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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