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 Q^\mu_{-(1/2)+i\lambda}(x).}

${\displaystyle Q_{-(1/2)+i\lambda }^{\mu }(x).}$

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

Semantic latex: \assLegendreOlverQ[\mu]{-(1/2)+i\lambda}@{x}

Confidence: 0.80962806770077

Mathematica

Translation: Exp[-(\[Mu]) Pi I] LegendreQ[-(1/2)+ i*\[Lambda], \[Mu], 3, x]/Gamma[-(1/2)+ i*\[Lambda] + \[Mu] + 1]

Information

Sub Equations

Exp[-(\[Mu]) Pi I] LegendreQ[-(1/2)+ i*\[Lambda], \[Mu], 3, x]/Gamma[-(1/2)+ i*\[Lambda] + \[Mu] + 1]

Free variables

\[Lambda]

\[Mu]

i

x

Symbol info

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

Olver's associated Legendre function; Example: \assLegendreOlverQ[\mu]{\nu}@{z}

Will be translated to: Alternative translations: [Exp[-($0) Pi I] LegendreQ[$1, $0, 3, $2]/Gamma[$1 + $0 + 1]]Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.3#E10 Mathematica:

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Maple

Translation: exp(-(mu)*Pi*I)*LegendreQ(-(1/2)+ i*lambda,mu,x)/GAMMA(-(1/2)+ i*lambda+mu+1)

Information

Sub Equations

exp(-(mu)*Pi*I)*LegendreQ(-(1/2)+ i*lambda,mu,x)/GAMMA(-(1/2)+ i*lambda+mu+1)

Free variables

i

lambda

mu

x

Symbol info

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

Olver's associated Legendre function; Example: \assLegendreOlverQ[\mu]{\nu}@{z}

Will be translated to: exp(-($0)*Pi*I)*LegendreQ($1,$0,$2)/GAMMA($1+$0+1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.3#E10 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreQ

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$P_{-(1/2)+i\lambda }^{\mu }(x)$

Is part of

$P_{-(1/2)+i\lambda }^{\mu }(x)$

Description

function

Gustav Ferdinand Mehler

term of Legendre function

distance of a point

series

axis of a cone

conical function

mathematics

Mehler function

point

surface of the cone

Complete translation information:

{
  "id" : "FORMULA_8247fb5c9658f8b4ff0218aea81e357c",
  "formula" : "Q^\\mu_{-(1/2)+i\\lambda}(x)",
  "semanticFormula" : "\\assLegendreOlverQ[\\mu]{-(1/2)+i\\lambda}@{x}",
  "confidence" : 0.8096280677007748,
  "translations" : {
    "Mathematica" : {
      "translation" : "Exp[-(\\[Mu]) Pi I] LegendreQ[-(1/2)+ i*\\[Lambda], \\[Mu], 3, x]/Gamma[-(1/2)+ i*\\[Lambda] + \\[Mu] + 1]",
      "translationInformation" : {
        "subEquations" : [ "Exp[-(\\[Mu]) Pi I] LegendreQ[-(1/2)+ i*\\[Lambda], \\[Mu], 3, x]/Gamma[-(1/2)+ i*\\[Lambda] + \\[Mu] + 1]" ],
        "freeVariables" : [ "\\[Lambda]", "\\[Mu]", "i", "x" ],
        "tokenTranslations" : {
          "i" : "You use a typical letter for a constant [the imaginary unit == the principal square root of -1].\nWe keep it like it is! But you should know that Mathematica uses I for this constant.\nIf you want to translate it as a constant, use the corresponding DLMF macro \\iunit\n",
          "\\assLegendreOlverQ1" : "Olver's associated Legendre function; Example: \\assLegendreOlverQ[\\mu]{\\nu}@{z}\nWill be translated to: \nAlternative translations: [Exp[-($0) Pi I] LegendreQ[$1, $0, 3, $2]/Gamma[$1 + $0 + 1]]Relevant links to definitions:\nDLMF:         http://dlmf.nist.gov/14.3#E10\nMathematica:  "
        }
      },
      "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: \\assLegendreOlverQ [\\assLegendreOlverQ]"
        }
      },
      "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" : "exp(-(mu)*Pi*I)*LegendreQ(-(1/2)+ i*lambda,mu,x)/GAMMA(-(1/2)+ i*lambda+mu+1)",
      "translationInformation" : {
        "subEquations" : [ "exp(-(mu)*Pi*I)*LegendreQ(-(1/2)+ i*lambda,mu,x)/GAMMA(-(1/2)+ i*lambda+mu+1)" ],
        "freeVariables" : [ "i", "lambda", "mu", "x" ],
        "tokenTranslations" : {
          "i" : "You use a typical letter for a constant [the imaginary unit == the principal square root of -1].\nWe keep it like it is! But you should know that Maple uses I for this constant.\nIf you want to translate it as a constant, use the corresponding DLMF macro \\iunit\n",
          "\\assLegendreOlverQ1" : "Olver's associated Legendre function; Example: \\assLegendreOlverQ[\\mu]{\\nu}@{z}\nWill be translated to: exp(-($0)*Pi*I)*LegendreQ($1,$0,$2)/GAMMA($1+$0+1)\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/14.3#E10\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreQ"
        }
      },
      "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" : 0,
    "word" : 32
  } ],
  "includes" : [ "P^\\mu_{-(1/2)+i\\lambda}(x)" ],
  "isPartOf" : [ "P^\\mu_{-(1/2)+i\\lambda}(x)" ],
  "definiens" : [ {
    "definition" : "function",
    "score" : 0.8221824402028584
  }, {
    "definition" : "Gustav Ferdinand Mehler",
    "score" : 0.6432331635625809
  }, {
    "definition" : "term of Legendre function",
    "score" : 0.6288842031023242
  }, {
    "definition" : "distance of a point",
    "score" : 0.6033992232315736
  }, {
    "definition" : "series",
    "score" : 0.6033992232315736
  }, {
    "definition" : "axis of a cone",
    "score" : 0.5074197820340112
  }, {
    "definition" : "conical function",
    "score" : 0.48771694939097315
  }, {
    "definition" : "mathematics",
    "score" : 0.48771694939097315
  }, {
    "definition" : "Mehler function",
    "score" : 0.44936883129115235
  }, {
    "definition" : "point",
    "score" : 0.4238838514204018
  }, {
    "definition" : "surface of the cone",
    "score" : 0.3719049079581628
  } ]
}

Specify your own input

Formula input
Wikitext context	In [[mathematics]], '''conical functions''' or '''Mehler functions''' are [[function (mathematics)\|functions]] which can be expressed in terms of [[Legendre function]]s of the first and second kind, <math>P^\mu_{-(1/2)+i\lambda}(x)</math> and <math>Q^\mu_{-(1/2)+i\lambda}(x).</math> The functions <math>P^\mu_{-(1/2)+i\lambda}(x)</math> were introduced by [[Gustav Ferdinand Mehler]], in 1868, when expanding in series the distance of a point on the axis of a cone to a point located on the surface of the cone. Mehler used the notation <math>K^\mu(x)</math> to represent these functions. He obtained integral representation and series of functions representations for them. He also established an addition theorem for the conical functions. [[Carl Neumann]] obtained an expansion of the functions <math>K^\mu(x)</math> in terms of the [[Legendre polynomials]] in 1881. Leonhardt introduced for the conical functions the equivalent of the [[spherical harmonics]] in 1882. ==External links== {{dlmf\|first=T. M. \|last=Dunster\|id=14.20\|title=Conical (or Mehler) Functions}} G. F. Mehler "[http://www.digizeitschriften.de/resolveppn/GDZPPN002153386 Ueber die Vertheilung der statischen Elektricität in einem von zwei Kugelkalotten begrenzten Körper]" ''Journal für die reine und angewandte Mathematik'' '''68''', 134 (1868). * G. F. Mehler "[http://www.digizeitschriften.de/resolveppn/GDZPPN002246112 Ueber eine mit den Kugel- und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie der Elektricitätsvertheilung]" ''Mathematische Annalen'' '''18''' p. 161 (1881). * C. Neumann "[http://www.digizeitschriften.de/resolveppn/GDZPPN002246120 Ueber die Mehler'schen Kegelfunctionen und deren Anwendung auf elektrostatische Probleme]" ''Mathematische Annalen'' '''18''' p. 195 (1881). * G. Leonhardt "[http://www.digizeitschriften.de/resolveppn/GDZPPN002246694 Integraleigenschaften der adjungirten Kegelfunctionen]" ''Mathematische Annalen'' '''19''' p. 578 (1882). * {{MathWorld\|title=Conical function\|urlname=ConicalFunction}} * Milton Abramowitz and Irene Stegun (Eds.) ''[[Abramowitz and Stegun\|Handbook of Mathematical Functions]]'' (Dover, 1972) [http://www.math.sfu.ca/~cbm/aands/page_337.htm p. 337] * A. Gil, J. Segura, N. M. Temme "[http://oai.cwi.nl/oai/asset/13868/13868A.pdf Computing the conical function $P^{\mu}_{-1/2+i\tau}(x)$]" ''SIAM J. Sci. Comput.'' 31(3), 1716–1741 (2009). * Tiwari, U. N.; Pandey, J. N. The Mehler-Fock transform of distributions. ''Rocky Mountain J. Math.'' 10 (1980), no. 2, 401–408. [[Category:Special functions]] {{mathanalysis-stub}}
	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