## General

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Hash: ddde7228ce5308aefe0f64f12f592fef

TeX (original user input):
{\displaystyle P_{n}}


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## Translations to Computer Algebra Systems

### Translation to Maple

In Maple: P[n]

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

\ChebyU: Chebyshev polynomial second kind; Example: \ChebyU{n}@{x}

\ChebyT: Chebyshev polynomial first kind; Example: \ChebyT{n}@{x}

\expe: Recognizes e with power as the exponential function. It was translated as a function.

\Laguerre1: Laguerre polynomial; Example: \Laguerre[\alpha]{n}@{x}

\digamma: Digamma / Psi function; Example: \digamma@{z}

Constraints: z not element of {0, -1, -2, ...}

\HyperpFq: Generalized hypergeometric function; Example: \HyperpFq{p}{q}@@@{a_1,...,a_p}{b_1,...,b_q}{z}

Translation Information: Maple extract p and q from the length of the arguments.

Maple: https://

\EulerGamma: Euler Gamma function; Example: \EulerGamma@{z}

\Dilogarithm: Dilogarithm; Example: \Dilogarithm@{z}

\ph: Argument of a complex number; Example: \ph@@{z}

Translation Information: arctan($0,$1) is an alternative. With the real part in the first argument and the complex part in the second.

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

\Hermite: Hermite polynomial; Example: \Hermite{n}@{x}

\Int: Integral; Example: \Int{a}{b}@{x}{f(x)}

\pochhammer: Pochhammer symbol; Example: \pochhammer{a}{n}

\RiemannZeta: Riemann zeta function; Example: \RiemannZeta@{s}

\ln: Natural logarithm; Example: \ln@@{z}

Constraints: z != 0

Branch Cuts: (-\infty, 0]

\pderiv: Partial derivative; Example: \pderiv{f}{x}

\exp: Exponential function; Example: \exp@@{z}

\Ultra: Ultraspherical Gegenbauer polynomial; Example: \Ultra{\lambda}{n}@{x}

\Jacobi: Jacobi polynomial; Example: \Jacobi{\alpha}{\beta}{n}@{x}

\HarmonicNumber: Harmonic number; Example: \HarmonicNumber{n}

Translation Information: DLMF assumes nonnegative integers.

\realpart: Real part of a complex number; Example: \realpart{z}

\HurwitzZeta: Hurwitz zeta function; Example: \HurwitzZeta@{s}{a}

\imagpart: Imaginary part of a complex num; Example: \imagpart{z}

\StieltjesConstants: Stieltjes Constants; Example: \StieltjesConstants{n}

\AntiDer: Anti-Derivative; Example: \AntiDer@{x}{f(x)}

\LerchPhi: Lerch Phi function; Example: \LerchPhi@{z}{s}{a}

\CatalansConstant: Catalan's constant was translated to: Catalan

\EulerConstant: Euler-Mascheroni constant was translated to: gamma

\alpha: Could be the second Feigenbaum constant.

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

\cpi: Pi was translated to: Pi

\delta: Could be the first Feigenbaum constant.

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

\gamma: Could be the Euler-Mascheroni 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 \EulerConstant to translate \gamma as a constant.

\iunit: Imaginary unit was translated to: I

\opminus: was translated to (-1)

\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.

\psi: Could be The reciprocal Fibonacci constant.

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

arctan: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

cos: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

cosh: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

cot: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

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 Maple uses exp(1) for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \expe

exp: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

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

ln: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

sin: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

### Translation to Mathematica

In Mathematica: Subscript[P, n]

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

\realpart: Real part of a complex number; Example: \realpart{z}

\expe: Recognizes e with power as the exponential function. It was translated as a function.

\ph: Argument of a complex number; Example: \ph@@{z}

\binomial: Binomial coefficient; Example: \binomial{m}{n}

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

\imagpart: Imaginary part of a complex num; Example: \imagpart{z}

\pochhammer: Pochhammer symbol; Example: \pochhammer{a}{n}

Mathematica: https://

\exp: Exponential function; Example: \exp@@{z}

\EulerGamma: Euler Gamma function; Example: \EulerGamma@{z}

\Jacobi: Jacobi polynomial; Example: \Jacobi{\alpha}{\beta}{n}@{x}

\ln: Natural logarithm; Example: \ln@@{z}

Constraints: z != 0

Branch Cuts: (-\infty, 0]

\CatalansConstant: Catalan's constant was translated to: Catalan

\EulerConstant: Euler-Mascheroni constant was translated to: EulerGamma

\alpha: Could be the second Feigenbaum constant.

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

\cpi: Pi was translated to: Pi

\delta: Could be the first Feigenbaum constant.

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

\gamma: Could be the Euler-Mascheroni 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 \EulerConstant to translate \gamma as a constant.

\iunit: Imaginary unit was translated to: I

\opminus: was translated to (-1)

\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.

\psi: Could be The reciprocal Fibonacci constant.

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

arctan: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

cos: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

cosh: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

cot: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

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

exp: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

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

ln: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

sin: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

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