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* Page found: Definition:ctsqLegendre (eq math.544.5) (force rerendering)

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

LaTeXML (experimental; uses MathML) rendering

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

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: P[n]

Information about the conversion process:

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

Relevant links to definitions:

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

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/18.3#T1.t1.r5

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/18.3#T1.t1.r4

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


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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/18.3#T1.t1.r12

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


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

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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/5.2#E2

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


\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.

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/16.2#E1

Maple: https://


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/5.2#E1

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/25.12#E1

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


\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.

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/1.9#E7

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


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

Relevant links to definitions:

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

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/18.3#T1.t1.r13

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


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

Relevant links to definitions:

DLMF: http://drmf.wmflabs.org/wiki/Definition:Int

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/5.2#iii

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/25.2#E1

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


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

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/1.5#E3

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E19

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/18.3#T1.t1.r3

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/18.3#T1.t1.r2

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


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

Translation Information: DLMF assumes nonnegative integers.

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/25.11#E33

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/1.9#E2

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/25.11#E1

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/1.9#E2

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


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

Relevant links to definitions:

DLMF: http://drmf.wmflabs.org/wiki/Definition:StieltjesConstants

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


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

Relevant links to definitions:

DLMF: http://drmf.wmflabs.org/wiki/Definition:AntiDer

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/25.14#E1

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


\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]

Information about the conversion process:

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

Relevant links to definitions:

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

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/1.9#E2

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


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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/1.9#E7

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/1.2#E1

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


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

Relevant links to definitions:

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

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/1.9#E2

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/5.2#iii

Mathematica: https://


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E19

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/5.2#E1

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


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

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/18.3#T1.t1.r2

Mathematica: https://reference.wolfram.com/language/ref/JacobiP.html?q=JacobiP


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

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

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


\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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