LaTeX to CAS translator
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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 s}
... is translated to the CAS output ...
Semantic latex: s
Confidence: 0
Mathematica
Translation: s
Information
Sub Equations
- s
Free variables
- s
Tests
Symbolic
Numeric
SymPy
Translation: s
Information
Sub Equations
- s
Free variables
- s
Tests
Symbolic
Numeric
Maple
Translation: s
Information
Sub Equations
- s
Free variables
- s
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
Description
- series
- Re
- series representation for the Lerch
- Pochhammer symbol
- digamma function
- positive integer
- polylogarithm
- special case
- Various identity
- n
- Taylor series in the third variable
- integral representation
- contour
- asymptotic series
- asymptotic series in the incomplete gamma function
- asymptotic expansion
- special case of the Lerch Zeta
- last formula
- finite sum over the Hurwitz zeta-function
- root of unity
- Dirichlet eta function
- Riemann zeta function
- Hurwitz zeta function
- Lipschitz formula
- Similar representation
- Hermite-like integral representation
- related function
- Lerch zeta function
- summand
- integral
- point
Complete translation information:
{
"id" : "FORMULA_03c7c0ace395d80182db07ae2c30f034",
"formula" : "s",
"semanticFormula" : "s",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "s",
"translationInformation" : {
"subEquations" : [ "s" ],
"freeVariables" : [ "s" ]
},
"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" : "s",
"translationInformation" : {
"subEquations" : [ "s" ],
"freeVariables" : [ "s" ]
},
"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" : "s",
"translationInformation" : {
"subEquations" : [ "s" ],
"freeVariables" : [ "s" ]
},
"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" : 5,
"sentence" : 2,
"word" : 6
}, {
"section" : 6,
"sentence" : 1,
"word" : 17
} ],
"includes" : [ ],
"isPartOf" : [ "\\,\\Phi(e^{2\\pi i\\lambda}, s,\\alpha)=L(\\lambda, \\alpha,s)", "\\Phi(z,s+1,a)=-\\,\\frac{1}{s}\\frac{\\partial}{\\partial a} \\Phi(z,s,a)", "\\Phi(-z,s,a)= \\frac{1}{2a^s} + \\int_{0}^{\\infty}\\frac{\\cos(t\\log z)\\sin\\Big(s\\arctan\\tfrac{t}{a}\\Big) - \\sin(t\\log z)\\cos\\Big(s\\arctan\\tfrac{t}{a}\\Big)}{\\big(a^2 + t^2\\big)^{\\frac{s}{2}} \\sinh\\pi t }\\,dt", "\\Phi(\\omega, s, \\alpha) = \\sum_{n=0}^\\infty\\frac {\\omega^n} {(n+\\alpha)^s} = \\sum_{m=0}^{q-1} \\sum_{n=0}^\\infty \\frac {\\omega^{qn + m}}{(qn + m + \\alpha)^s} = \\sum_{m=0}^{q-1} \\omega^m q^{-s} \\zeta(s,\\frac{m + \\alpha}{q})", "\\,\\eta(s)=\\Phi (-1,s,1)", "\\Phi(z,s,a)=-\\frac{\\Gamma(1-s)}{2\\pi i}\\int_0^{(+\\infty)}\\frac{(-t)^{s-1}e^{-at}}{1-ze^{-t}}\\,dt", "\\,\\zeta(s,\\alpha)=L(0, \\alpha,s)=\\Phi(1,s,\\alpha)", "L(\\lambda, \\alpha, s) = \\sum_{n=0}^\\infty\\frac { e^{2\\pi i\\lambda n}} {(n+\\alpha)^s}", "\\Phi(e^{i\\varphi},s,a)=L\\big(\\tfrac{\\varphi}{2\\pi},a,s\\big)= \\frac{1}{a^s} + \\frac{1}{2\\Gamma(s)}\\int_{0}^{\\infty}\\frac{t^{s-1}e^{-at}\\big(e^{i\\varphi}-e^{-t}\\big)}{\\cosh{t}-\\cos{\\varphi}}\\,dt", "\\,\\textrm{Li}_s(z)=z\\Phi(z,s,1)", "L(\\lambda, \\alpha, s)", "\\Phi(z,s,a)=\\frac{1}{\\Gamma(s)}\\int_0^\\infty\\frac{t^{s-1}e^{-at}}{1-ze^{-t}}\\,dt", "\\Phi(z,s,a)=\\frac{1}{2a^s}+\\frac{\\log^{s-1}(1/z)}{z^a}\\Gamma(1-s,a\\log(1/z))+\\frac{2}{a^{s-1}}\\int_0^\\infty\\frac{\\sin(s\\arctan(t)-ta\\log(z))}{(1+t^2)^{s/2}(e^{2\\pi at}-1)}\\,dt", "\\Phi(z,s,a)=z^n \\Phi(z,s,a+n) + \\sum_{k=0}^{n-1} \\frac {z^k}{(k+a)^s}", "\\Re(a)>0\\wedge\\Re(s)<0\\wedge z<1", "\\,\\zeta(s)=\\Phi (1,s,1)", "\\Phi(z,s,q)=\\frac{1}{1-z} \\sum_{n=0}^\\infty \\left(\\frac{-z}{1-z} \\right)^n\\sum_{k=0}^n (-1)^k \\binom{n}{k} (q+k)^{-s}", "\\Phi(z,s-1,a)=\\left(a+z\\frac{\\partial}{\\partial z}\\right) \\Phi(z,s,a)", "\\Re(a)>0\\wedge\\Re(s)>0\\wedge z<1\\vee\\Re(a)>0\\wedge\\Re(s)>1\\wedge z=1", "\\Phi(z,s,a)= \\frac{1}{2a^s} + \\int_{0}^{\\infty}\\frac{\\cos(t\\log z)\\sin\\Big(s\\arctan\\tfrac{t}{a}\\Big) - \\sin(t\\log z)\\cos\\Big(s\\arctan\\tfrac{t}{a}\\Big)}{\\big(a^2 + t^2\\big)^{\\frac{s}{2}} \\tanh\\pi t }\\,dt", "\\Phi(z, s, \\alpha) = \\sum_{n=0}^\\infty\\frac { z^n} {(n+\\alpha)^s}", "\\Phi(z,s,a)=\\frac{1}{2a^s}+\\int_0^\\infty \\frac{z^t}{(a+t)^s}\\,dt+\\frac{2}{a^{s-1}}\\int_0^\\infty\\frac{\\sin(s\\arctan(t)-ta\\log(z))}{(1+t^2)^{s/2}(e^{2\\pi at}-1)}\\,dt", "|\\log(z)|<2 \\pi;s\\neq 1,2,3,\\dots; a\\neq 0,-1,-2,\\dots", "\\Phi(z,s,a)=z^{-a}\\left[\\Gamma(1-s)\\left(-\\log (z)\\right)^{s-1}+\\sum_{k=0}^\\infty \\zeta(s-k,a)\\frac{\\log^k (z)}{k!}\\right]", "\\Phi(z,s,a+x)=\\sum_{k=0}^\\infty \\Phi(z,s+k,a)(s)_{k}\\frac{(-x)^k}{k!};|x|<\\Re(a)", "(s)_{k}", "\\Phi(z,s,a)=\\sum_{k=0}^n \\frac{z^k}{(a+k)^s}+z^n\\sum_{m=0}^\\infty (1-m-s)_{m}\\operatorname{Li}_{s+m}(z)\\frac{(a+n)^m}{m!};\\ a\\rightarrow-n", "\\Phi(z,s,a)=\\frac{1}{a^s}+\\sum_{m=0}^\\infty (1-m-s)_m \\operatorname{Li}_{s+m}(z)\\frac{a^m}{m!}; |a|<1", "\\operatorname{Li}_s(z)", "s\\rightarrow-\\infty", "\\Phi(z,s,a)=z^{-a}\\Gamma(1-s)\\sum_{k=-\\infty}^\\infty[2k\\pi i-\\log(z)]^{s-1}e^{2k\\pi ai}", "|a|<1;\\Re(s)<0 ;z\\notin (-\\infty,0)", "\\Phi(-z,s,a)=z^{-a}\\Gamma(1-s)\\sum_{k=-\\infty}^\\infty[(2k+1)\\pi i-\\log(z)]^{s-1}e^{(2k+1)\\pi ai}", "|a|<1;\\Re(s)<0 ;z\\notin (0,\\infty)", "\\Phi(z,s,a)=\\frac{1}{2a^s}+\\frac{1}{z^a}\\sum_{k=1}^\\infty\\frac{e^{-2\\pi i(k-1)a}\\Gamma(1-s,a(-2\\pi i(k-1)-\\log(z)))} {(-2\\pi i(k-1)-\\log(z))^{1-s}}+\\frac{e^{2\\pi ika}\\Gamma(1-s,a(2\\pi ik-\\log(z)))}{(2\\pi ik-\\log(z))^{1-s}}", "|a|<1;\\Re(s)<0", "|\\mathrm{Arg}(a)|<\\pi, s \\in \\mathbb{C}", "\\Phi(z,s,a)", "\\Phi(z,s,a) = \\frac{1}{1-z} \\frac{1}{a^{s}} + \\sum_{n=1}^{N-1} \\frac{(-1)^{n} \\mathrm{Li}_{-n}(z)}{n!} \\frac{(s)_{n}}{a^{n+s}} +O(a^{-N-s})", "(s)_n = s (s+1)\\cdots (s+n-1)", "\\Re s > 0", "\\Phi(z,s,a) - \\frac{\\mathrm{Li}_{s}(z)}{z^{a}}=\\sum_{n=0}^{N-1}C_{n}(z,a) \\frac{(s)_{n}}{a^{n+s}}+O\\left( (\\Re a)^{1-N-s}+a z^{-\\Re a} \\right)" ],
"definiens" : [ {
"definition" : "series",
"score" : 0.8578493177812476
}, {
"definition" : "Re",
"score" : 0.6601229053380933
}, {
"definition" : "series representation for the Lerch",
"score" : 0.5689677394864224
}, {
"definition" : "Pochhammer symbol",
"score" : 0.5322214723345956
}, {
"definition" : "digamma function",
"score" : 0.48821814343333136
}, {
"definition" : "positive integer",
"score" : 0.48821814343333136
}, {
"definition" : "polylogarithm",
"score" : 0.4759628194570583
}, {
"definition" : "special case",
"score" : 0.4553642978243066
}, {
"definition" : "Various identity",
"score" : 0.45267071030642325
}, {
"definition" : "n",
"score" : 0.44838420310232413
}, {
"definition" : "Taylor series in the third variable",
"score" : 0.416579329930231
}, {
"definition" : "integral representation",
"score" : 0.39913290968719844
}, {
"definition" : "contour",
"score" : 0.3900329792440058
}, {
"definition" : "asymptotic series",
"score" : 0.36449136763412854
}, {
"definition" : "asymptotic series in the incomplete gamma function",
"score" : 0.35089872108221626
}, {
"definition" : "asymptotic expansion",
"score" : 0.34315870430225354
}, {
"definition" : "special case of the Lerch Zeta",
"score" : 0.3430341139924638
}, {
"definition" : "last formula",
"score" : 0.3430040373645118
}, {
"definition" : "finite sum over the Hurwitz zeta-function",
"score" : 0.3242088302147525
}, {
"definition" : "root of unity",
"score" : 0.3242088302147525
}, {
"definition" : "Dirichlet eta function",
"score" : 0.31880029202809124
}, {
"definition" : "Riemann zeta function",
"score" : 0.31698488450476003
}, {
"definition" : "Hurwitz zeta function",
"score" : 0.31631862764557106
}, {
"definition" : "Lipschitz formula",
"score" : 0.316314146497048
}, {
"definition" : "Similar representation",
"score" : 0.3163134771496293
}, {
"definition" : "Hermite-like integral representation",
"score" : 0.31631339177489187
}, {
"definition" : "related function",
"score" : 0.31631338152885907
}, {
"definition" : "Lerch zeta function",
"score" : 0.3163133815285839
}, {
"definition" : "summand",
"score" : 0.28437488988374526
}, {
"definition" : "integral",
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}, {
"definition" : "point",
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} ]
}