LaTeX to CAS translator

This mockup demonstrates the concept of TeX to Computer Algebra System (CAS) conversion.

The demo-application converts LaTeX functions which directly translate to CAS counterparts.

Functions without explicit CAS support are available for translation via a DRMF package (under development).

The following LaTeX input ...

{\displaystyle M_n(x,\beta,\gamma) = \sum_{k=0}^n (-1)^k{n \choose k}{x\choose k}k!(x+\beta)_{n-k}\gamma^{-k}}

${\displaystyle M_{n}(x,\beta ,\gamma )=\sum _{k=0}^{n}(-1)^{k}{n \choose k}{x \choose k}k!(x+\beta )_{n-k}\gamma ^{-k}}$

... is translated to the CAS output ...

Semantic latex: M_n(x , \beta , \gamma) = \sum_{k=0}^n(- 1)^k{n \choose k}{x\choose k} k! \Pochhammersym{x + \beta}{n-k} \gamma^{-k}

Confidence: 0.89530287320794

Mathematica

Translation: Subscript[M, n][x , \[Beta], \[Gamma]] == Sum[(- 1)^(k)*Binomial[n,k]*Binomial[x,k]*(k)!*Pochhammer[x + \[Beta], n - k]*\[Gamma]^(- k), {k, 0, n}, GenerateConditions->None]

Information

Sub Equations

Subscript[M, n][x , \[Beta], \[Gamma]] = Sum[(- 1)^(k)*Binomial[n,k]*Binomial[x,k]*(k)!*Pochhammer[x + \[Beta], n - k]*\[Gamma]^(- k), {k, 0, n}, GenerateConditions->None]

Free variables

\[Beta]

\[Gamma]

n

x

Symbol info

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.

Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

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

Will be translated to: Pochhammer[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#iii Mathematica: https://reference.wolfram.com/language/ref/Pochhammer.html

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \Pochhammersym [\Pochhammersym]

Tests

Symbolic

Numeric

Maple

Translation: M[n](x , beta , gamma) = sum((- 1)^(k)*binomial(n,k)*binomial(x,k)*factorial(k)*pochhammer(x + beta, n - k)*(gamma)^(- k), k = 0..n)

Information

Sub Equations

M[n](x , beta , gamma) = sum((- 1)^(k)*binomial(n,k)*binomial(x,k)*factorial(k)*pochhammer(x + beta, n - k)*(gamma)^(- k), k = 0..n)

Free variables

beta

gamma

n

x

Symbol info

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.

Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

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

Will be translated to: pochhammer($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#iii Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=pochhammer

Tests

Symbolic

Numeric

Dependency Graph Information

Description

Pochhammer symbol

term of binomial coefficient

Complete translation information:

{
  "id" : "FORMULA_29a1f82de004c5721c8dfc5dd1dc5b98",
  "formula" : "M_n(x,\\beta,\\gamma) = \\sum_{k=0}^n (-1)^k{n \\choose k}{x\\choose k}k!(x+\\beta)_{n-k}\\gamma^{-k}",
  "semanticFormula" : "M_n(x , \\beta , \\gamma) = \\sum_{k=0}^n(- 1)^k{n \\choose k}{x\\choose k} k! \\Pochhammersym{x + \\beta}{n-k} \\gamma^{-k}",
  "confidence" : 0.8953028732079359,
  "translations" : {
    "Mathematica" : {
      "translation" : "Subscript[M, n][x , \\[Beta], \\[Gamma]] == Sum[(- 1)^(k)*Binomial[n,k]*Binomial[x,k]*(k)!*Pochhammer[x + \\[Beta], n - k]*\\[Gamma]^(- k), {k, 0, n}, GenerateConditions->None]",
      "translationInformation" : {
        "subEquations" : [ "Subscript[M, n][x , \\[Beta], \\[Gamma]] = Sum[(- 1)^(k)*Binomial[n,k]*Binomial[x,k]*(k)!*Pochhammer[x + \\[Beta], n - k]*\\[Gamma]^(- k), {k, 0, n}, GenerateConditions->None]" ],
        "freeVariables" : [ "\\[Beta]", "\\[Gamma]", "n", "x" ],
        "tokenTranslations" : {
          "\\gamma" : "Could be the Euler-Mascheroni constant.\nBut it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!\nUse the DLMF-Macro \\EulerConstant to translate \\gamma as a constant.\n",
          "M" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\Pochhammersym" : "Pochhammer symbol; Example: \\Pochhammersym{a}{n}\nWill be translated to: Pochhammer[$0, $1]\nRelevant links to definitions:\nDLMF:         http://dlmf.nist.gov/5.2#iii\nMathematica:  https://reference.wolfram.com/language/ref/Pochhammer.html"
        }
      },
      "numericResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "wasAborted" : false,
        "crashed" : false,
        "testCalculationsGroups" : [ ]
      },
      "symbolicResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "crashed" : false,
        "testCalculationsGroup" : [ ]
      }
    },
    "SymPy" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\Pochhammersym [\\Pochhammersym]"
        }
      },
      "numericResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "wasAborted" : false,
        "crashed" : false,
        "testCalculationsGroups" : [ ]
      },
      "symbolicResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "crashed" : false,
        "testCalculationsGroup" : [ ]
      }
    },
    "Maple" : {
      "translation" : "M[n](x , beta , gamma) = sum((- 1)^(k)*binomial(n,k)*binomial(x,k)*factorial(k)*pochhammer(x + beta, n - k)*(gamma)^(- k), k = 0..n)",
      "translationInformation" : {
        "subEquations" : [ "M[n](x , beta , gamma) = sum((- 1)^(k)*binomial(n,k)*binomial(x,k)*factorial(k)*pochhammer(x + beta, n - k)*(gamma)^(- k), k = 0..n)" ],
        "freeVariables" : [ "beta", "gamma", "n", "x" ],
        "tokenTranslations" : {
          "\\gamma" : "Could be the Euler-Mascheroni constant.\nBut it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!\nUse the DLMF-Macro \\EulerConstant to translate \\gamma as a constant.\n",
          "M" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\Pochhammersym" : "Pochhammer symbol; Example: \\Pochhammersym{a}{n}\nWill be translated to: pochhammer($0, $1)\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/5.2#iii\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=pochhammer"
        }
      },
      "numericResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "wasAborted" : false,
        "crashed" : false,
        "testCalculationsGroups" : [ ]
      },
      "symbolicResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "crashed" : false,
        "testCalculationsGroup" : [ ]
      }
    }
  },
  "positions" : [ {
    "section" : 0,
    "sentence" : 1,
    "word" : 16
  } ],
  "includes" : [ ],
  "isPartOf" : [ ],
  "definiens" : [ {
    "definition" : "Pochhammer symbol",
    "score" : 0.6859086196238077
  }, {
    "definition" : "term of binomial coefficient",
    "score" : 0.6460746792928004
  } ]
}

Specify your own input

Formula input
Wikitext context	{{distinguish\|Meixner–Pollaczek polynomials}} In mathematics, '''Meixner polynomials''' (also called '''discrete Laguerre polynomials''') are a family of [[discrete orthogonal polynomials]] introduced by {{harvs\|txt\|authorlink=Josef Meixner\|first=Josef\|last= Meixner\|year=1934}}. They are given in terms of [[binomial coefficient]]s and the (rising) [[Pochhammer symbol]] by :<math>M_n(x,\beta,\gamma) = \sum_{k=0}^n (-1)^k{n \choose k}{x\choose k}k!(x+\beta)_{n-k}\gamma^{-k}</math> ==See also== [[Kravchuk polynomials]] ==References== {{cite journal\| last1=Meixner \| first1=J. \| title=Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion \| doi=10.1112/jlms/s1-9.1.6 \| year=1934 \| journal=Journal of the London Mathematical Society \| volume=s1-9 \| pages=6–13}} {{cite journal \| first1=W. A. \| last1=Al-Salam \|title=On a characterization of Meixner's Polynomials \|journal=Quart. J. Math. \| year=1966 \| volume=17 \| number=1 \| pages=7–10 \|doi=10.1093/qmath/17.1.7 \|bibcode=1966QJMat..17....7A}} {{cite journal\| first1=N. M. \|last1=Atakishiyev \| first2=S. K. \| last2=Suslov \|title=The Hahn and Meixner polynomials of an imaginary argument and some of their applications \|year=1985 \| journal= J. Phys. A: Math. Gen. \|doi=10.1088/0305-4470/18/10/014 \|volume=18 \| number=10 \| pages=1583 \|bibcode=1985JPhA...18.1583A}} {{cite journal\| first1= G. E. \| last1=Andrews \| first2=Richard \| last2=Askey \|title=Classical orthogonal polynomials \|year=1985 \| journal = Lect. Notes Math. \| volume=1171 \| pages = 36–82 \|doi=10.1007/BFb0076530 \| series=Lecture Notes in Mathematics \| isbn=978-3-540-16059-5 }} {{cite journal \| first1= M. V. \| last1=Tratnik \|title=Multivariable Meixer, Krawtchouk, and Meixner-Pollaczek polynomials \|year=1989 \| journal= J. Math. Phys. \| volume=30 \| number=12 \| pages=2740 \| doi=10.1063/1.528507 \| bibcode=1989JMP....30.2740T\| url=https://zenodo.org/record/1232297 }} {{cite journal \| first1= M. V. \| last1=Tratnik \|title=Some multivariable orthogonal polynomials of the Askey tableau-discrete families \|journal = J. Math. Phys. \| year=1991 \| volume=32 \| number=9 \|pages=2337–2342 \| doi=10.1063/1.529158 \|bibcode=1991JMP....32.2337T\| url=https://zenodo.org/record/1232107 }} {{cite journal \| first1=H. \| last1=Bavinck \| first2=H. \| last2=Vanhaeringen \|title=Difference equations for generalized Meixner Polynomials \|journal= J. Math. Anal. Appl. \| year=1994 \| volume=184 \| number=3 \|doi=10.1006/jmaa.1994.1214 \| pages=453–463 }} {{cite journal \| first1= X.-S. \| last1=Jin \| first2=R. \|last2=Wong \|title= Uniform asymptotic expansion for Meixner polynomials \|year=1998 \| volume=14 \| number=1 \| pages=113–150 \|journal=Construct. Approx. \| doi=10.1007/s003659900066 }} {{cite journal \| first1=Maria \| last1=Álvarez de Morales \| first2=T. E. \| last2=Pérez \| first3=M. A. \| last3=Piñar \| first4=A. \| last4=Ronveaux \| title=Non-standard orthogonality for Meixner Polynomials \| year=1999 \| journal=El. Trans. Num. Anal. \| volume=9 \| pages=1–25 \| url=http://www.emis.ams.org/journals/ETNA/vol.9.1999/pp1-25.dir/pp1-25.pdf \| access-date=2013-03-10 \| archive-url=https://web.archive.org/web/20081122043419/http://www.emis.ams.org/journals/ETNA/vol.9.1999/pp1-25.dir/pp1-25.pdf \| archive-date=2008-11-22 \| url-status=dead }} {{cite journal\| first1=X.-S. \| last1=Jin \| first2=R. \| last2=Wong \|title=Asymptotic formulas for the zeros of Meixner Polynomials \|journal= J. Approx. Theory \| year=1999 \| volume=96 \| number=2 \| pages=281–300 \|doi=10.1006/jath.1998.3235 }} {{cite arXiv\| eprint=math/0609806 \| first1=Alexei \| last1=Borodin \|first2=Grigori \|last2=Olshanski \| title=Meixner polynomials and random partitions \|year=2006 }} {{dlmf\|id=18.19\|title=Hahn Class: Definitions\|first=Tom H. \|last=Koornwinder\|first2=Roderick S. C.\|last2= Wong\|first3=Roelof \|last3=Koekoek\|\|first4=René F. \|last4=Swarttouw}} {{cite journal \| first1=L. \|last1=Boelen \| first2=Galina \| last2=Filipuk \|first3=Walter \| last3= Van Assche \| journal=J. Phys. A: Math. Theor. \|title=Recurrence coefficients of generalized Meixner polynomials and Peinlevé equations \|year=2011 \| volume=44 \|number=3 \| pages=035202 \| doi=10.1088/1751-8113/44/3/035202 \|bibcode=2011JPhA...44c5202B}} *{{cite journal \| first1= Xiang-Sheng \| last1=Wang \| first2=Roderick \| last2=Wong \|title= Global asymptotics of the Meixner polynomials \|journal = Asymptot. Anal. \| year=2011 \| volume=75 \| number=3–4 \|pages=211–231 \| doi=10.3233/ASY-2011-1060 \|arxiv=1101.4370}} [[Category:Orthogonal polynomials]]
	Purge cached results.

LaTeX to CAS translator

Mathematica

Information

Tests

Symbolic

Numeric

SymPy

Information

Tests

Symbolic

Numeric

Maple

Information

Tests

Symbolic

Numeric

Dependency Graph Information

Specify your own input

Navigation menu

Search