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Display information for equation id:math.233568.10 on revision:233568

* Page found: Noncrossing partition (eq math.233568.10)

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Hash: 3cc5a131e96b8fd773c6f0a91fef6dd3

TeX (original user input):

\phi(a^n) = \sum_{\pi\in\text{NC}(n)} \prod_{j} k_j^{N_j(\pi)}

TeX (checked):

\phi (a^{n})=\sum _{\pi \in {\text{NC}}(n)}\prod _{j}k_{j}^{N_{j}(\pi )}

LaTeXML (experimental; uses MathML) rendering

MathML (7.272 KB / 1.269 KB) :

ϕ ( a n ) = π NC ( n ) j k j N j ( π ) italic-ϕ superscript 𝑎 𝑛 subscript 𝜋 NC 𝑛 subscript product 𝑗 superscript subscript 𝑘 𝑗 subscript 𝑁 𝑗 𝜋 {\displaystyle\phi(a^{n})=\sum_{{\pi\in{\text{NC}}(n)}}\prod_{{j}}k_{j}^{{N_{j% }(\pi)}}}
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SVG (12.374 KB / 4.486 KB) :

phi times left-parenthesis a Superscript n Baseline right-parenthesis equals sigma-summation Underscript pi element-of NC times left-parenthesis n right-parenthesis Endscripts product Underscript j Endscripts k Subscript j Superscript upper N Super Subscript j Superscript times left-parenthesis pi right-parenthesis

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

MathML (0 B / 8 B) :

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: phi*((a)^(n))sum(product(k(k[j])^(N[j]*(pi)), = - infinity..infinity), pi in N*C)

Information about the conversion process:

\phi: Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.

But this system don't know how to translate it as a constant. It was translated as a general letter.


\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.



Translation to Mathematica

In Mathematica: \[Phi]*((a)^(n))Sum[Product[k(Subscript[k, j])^(Subscript[N, j]*(\[Pi])), {, - Infinity, Infinity}], {\[Pi], N*C}]

Information about the conversion process:

\phi: Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.

But this system don't know how to translate it as a constant. It was translated as a general letter.


\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.



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