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 \mathbf{M}_\alpha(x)=-\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^1(1-t^2)^{\alpha-\frac{1}{2}}e^{-xt}~dt=-\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^\frac{\pi}{2}e^{-x\cos\tau}\sin^{2\alpha}\tau~d\tau=-\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^\frac{\pi}{2}e^{-x\sin\tau}\cos^{2\alpha}\tau~d\tau}
... is translated to the CAS output ...
Semantic latex: \modStruveM{\alpha}@{x} = - \frac{2(\frac{x}{2})^\alpha}{\sqrt{\cpi} \EulerGamma@{\alpha + \frac{1}{2}}} \int_0^1(1 - t^2)^{\alpha-\frac{1}{2}} \expe^{-xt} \diff{t} = - \frac{2(\frac{x}{2})^\alpha}{\sqrt{\cpi} \EulerGamma@{\alpha + \frac{1}{2}}} \int_0^{\frac{\cpi}{2}} \expe^{-x\cos\tau} \sin^{2\alpha} \tau \diff{\tau} = - \frac{2(\frac{x}{2})^\alpha}{\sqrt{\cpi} \EulerGamma@{\alpha + \frac{1}{2}}} \int_0^{\frac{\cpi}{2}} \expe^{-x\sin\tau} \cos^{2\alpha} \tau \diff{\tau}
Confidence: 0.65277464206746
Mathematica
Translation: StruveL[\[Alpha], x] - BesselI[\[Alpha], x] == -Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None] == -Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\[Tau]]]*(Sin[\[Tau]])^(2*\[Alpha]), {\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None] == -Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Sin[\[Tau]]]*(Cos[\[Tau]])^(2*\[Alpha]), {\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None]
Information
Sub Equations
- StruveL[\[Alpha], x] - BesselI[\[Alpha], x] = -Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None]
- -Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None] = -Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\[Tau]]]*(Sin[\[Tau]])^(2*\[Alpha]), {\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None]
- -Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\[Tau]]]*(Sin[\[Tau]])^(2*\[Alpha]), {\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None] = -Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Sin[\[Tau]]]*(Cos[\[Tau]])^(2*\[Alpha]), {\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None]
Free variables
- \[Alpha]
- x
Symbol info
- Cosine; Example: \cos@@{z}
Will be translated to: Cos[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 Mathematica: https://reference.wolfram.com/language/ref/Cos.html
- Recognizes e with power as the exponential function. It was translated as a function.
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- Sine; Example: \sin@@{z}
Will be translated to: Sin[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 Mathematica: https://reference.wolfram.com/language/ref/Sin.html
- Pi was translated to: Pi
- Associated Modified Struve function; Example: \modStruveM{\nu}@{z}
Will be translated to: StruveL[$0, $1] - BesselI[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.2#E6 Mathematica: https://reference.wolfram.com/language/ref/StruveL.html
- Euler Gamma function; Example: \EulerGamma@{z}
Will be translated to: Gamma[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#E1 Mathematica: https://reference.wolfram.com/language/ref/Gamma.html
Tests
Symbolic
Test expression: (StruveL[\[Alpha], x] - BesselI[\[Alpha], x])-(-Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Test expression: (-Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None])-(-Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\[Tau]]]*(Sin[\[Tau]])^(2*\[Alpha]), {\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Test expression: (-Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\[Tau]]]*(Sin[\[Tau]])^(2*\[Alpha]), {\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None])-(-Divide[2*(Divide[x,2])^\[Alpha],Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Sin[\[Tau]]]*(Cos[\[Tau]])^(2*\[Alpha]), {\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \modStruveM [\modStruveM]
Tests
Symbolic
Numeric
Maple
Translation: StruveL(alpha, x) - BesselI(alpha, x) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int((1 - (t)^(2))^(alpha -(1)/(2))* exp(- x*t), t = 0..1) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int(exp(- x*cos(tau))*(sin(tau))^(2*alpha), tau = 0..(Pi)/(2)) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int(exp(- x*sin(tau))*(cos(tau))^(2*alpha), tau = 0..(Pi)/(2))
Information
Sub Equations
- StruveL(alpha, x) - BesselI(alpha, x) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int((1 - (t)^(2))^(alpha -(1)/(2))* exp(- x*t), t = 0..1)
- -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int((1 - (t)^(2))^(alpha -(1)/(2))* exp(- x*t), t = 0..1) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int(exp(- x*cos(tau))*(sin(tau))^(2*alpha), tau = 0..(Pi)/(2))
- -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int(exp(- x*cos(tau))*(sin(tau))^(2*alpha), tau = 0..(Pi)/(2)) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int(exp(- x*sin(tau))*(cos(tau))^(2*alpha), tau = 0..(Pi)/(2))
Free variables
- alpha
- x
Symbol info
- Cosine; Example: \cos@@{z}
Will be translated to: cos($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos
- Recognizes e with power as the exponential function. It was translated as a function.
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- Sine; Example: \sin@@{z}
Will be translated to: sin($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin
- Pi was translated to: Pi
- Associated Modified Struve function; Example: \modStruveM{\nu}@{z}
Will be translated to: StruveL($0, $1) - BesselI($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.2#E6 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=StruveL
- Euler Gamma function; Example: \EulerGamma@{z}
Will be translated to: GAMMA($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GAMMA
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Complete translation information:
{
"id" : "FORMULA_3a45db51c42e69859d5020cec75ca85d",
"formula" : "\\mathbf{M}_\\alpha(x)=-\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^1(1-t^2)^{\\alpha-\\frac{1}{2}}e^{-xt}~dt=-\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^\\frac{\\pi}{2}e^{-x\\cos\\tau}\\sin^{2\\alpha}\\tau~d\\tau=-\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^\\frac{\\pi}{2}e^{-x\\sin\\tau}\\cos^{2\\alpha}\\tau~d\\tau",
"semanticFormula" : "\\modStruveM{\\alpha}@{x} = - \\frac{2(\\frac{x}{2})^\\alpha}{\\sqrt{\\cpi} \\EulerGamma@{\\alpha + \\frac{1}{2}}} \\int_0^1(1 - t^2)^{\\alpha-\\frac{1}{2}} \\expe^{-xt} \\diff{t} = - \\frac{2(\\frac{x}{2})^\\alpha}{\\sqrt{\\cpi} \\EulerGamma@{\\alpha + \\frac{1}{2}}} \\int_0^{\\frac{\\cpi}{2}} \\expe^{-x\\cos\\tau} \\sin^{2\\alpha} \\tau \\diff{\\tau} = - \\frac{2(\\frac{x}{2})^\\alpha}{\\sqrt{\\cpi} \\EulerGamma@{\\alpha + \\frac{1}{2}}} \\int_0^{\\frac{\\cpi}{2}} \\expe^{-x\\sin\\tau} \\cos^{2\\alpha} \\tau \\diff{\\tau}",
"confidence" : 0.6527746420674619,
"translations" : {
"Mathematica" : {
"translation" : "StruveL[\\[Alpha], x] - BesselI[\\[Alpha], x] == -Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None] == -Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\\[Tau]]]*(Sin[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None] == -Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Sin[\\[Tau]]]*(Cos[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "StruveL[\\[Alpha], x] - BesselI[\\[Alpha], x] = -Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None]", "-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None] = -Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\\[Tau]]]*(Sin[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None]", "-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\\[Tau]]]*(Sin[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None] = -Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Sin[\\[Tau]]]*(Cos[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[Alpha]", "x" ],
"tokenTranslations" : {
"\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: Cos[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E2\nMathematica: https://reference.wolfram.com/language/ref/Cos.html",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: Sin[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E1\nMathematica: https://reference.wolfram.com/language/ref/Sin.html",
"\\cpi" : "Pi was translated to: Pi",
"\\modStruveM" : "Associated Modified Struve function; Example: \\modStruveM{\\nu}@{z}\nWill be translated to: StruveL[$0, $1] - BesselI[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.2#E6\nMathematica: https://reference.wolfram.com/language/ref/StruveL.html",
"\\EulerGamma" : "Euler Gamma function; Example: \\EulerGamma@{z}\nWill be translated to: Gamma[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#E1\nMathematica: https://reference.wolfram.com/language/ref/Gamma.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 3,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 3,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "StruveL[\\[Alpha], x] - BesselI[\\[Alpha], x]",
"rhs" : "-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None]",
"testExpression" : "(StruveL[\\[Alpha], x] - BesselI[\\[Alpha], x])-(-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
}, {
"lhs" : "-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None]",
"rhs" : "-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\\[Tau]]]*(Sin[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None]",
"testExpression" : "(-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\\[Alpha]-Divide[1,2])* Exp[- x*t], {t, 0, 1}, GenerateConditions->None])-(-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\\[Tau]]]*(Sin[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
}, {
"lhs" : "-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\\[Tau]]]*(Sin[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None]",
"rhs" : "-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Sin[\\[Tau]]]*(Cos[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None]",
"testExpression" : "(-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Cos[\\[Tau]]]*(Sin[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None])-(-Divide[2*(Divide[x,2])^\\[Alpha],Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]*Integrate[Exp[- x*Sin[\\[Tau]]]*(Cos[\\[Tau]])^(2*\\[Alpha]), {\\[Tau], 0, Divide[Pi,2]}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\modStruveM [\\modStruveM]"
}
}
},
"Maple" : {
"translation" : "StruveL(alpha, x) - BesselI(alpha, x) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int((1 - (t)^(2))^(alpha -(1)/(2))* exp(- x*t), t = 0..1) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int(exp(- x*cos(tau))*(sin(tau))^(2*alpha), tau = 0..(Pi)/(2)) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int(exp(- x*sin(tau))*(cos(tau))^(2*alpha), tau = 0..(Pi)/(2))",
"translationInformation" : {
"subEquations" : [ "StruveL(alpha, x) - BesselI(alpha, x) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int((1 - (t)^(2))^(alpha -(1)/(2))* exp(- x*t), t = 0..1)", "-(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int((1 - (t)^(2))^(alpha -(1)/(2))* exp(- x*t), t = 0..1) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int(exp(- x*cos(tau))*(sin(tau))^(2*alpha), tau = 0..(Pi)/(2))", "-(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int(exp(- x*cos(tau))*(sin(tau))^(2*alpha), tau = 0..(Pi)/(2)) = -(2*((x)/(2))^(alpha))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))*int(exp(- x*sin(tau))*(cos(tau))^(2*alpha), tau = 0..(Pi)/(2))" ],
"freeVariables" : [ "alpha", "x" ],
"tokenTranslations" : {
"\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: cos($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: sin($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin",
"\\cpi" : "Pi was translated to: Pi",
"\\modStruveM" : "Associated Modified Struve function; Example: \\modStruveM{\\nu}@{z}\nWill be translated to: StruveL($0, $1) - BesselI($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.2#E6\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=StruveL",
"\\EulerGamma" : "Euler Gamma function; Example: \\EulerGamma@{z}\nWill be translated to: GAMMA($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GAMMA"
}
}
}
},
"positions" : [ ],
"includes" : [ "\\mathbf{K}_\\alpha(x)", "\\alpha", "\\Gamma(z)", "\\mathbf{H}_{\\alpha}(x)", "\\mathbf{L}_{\\alpha}(x)", "x", "\\mathbf{H}_{\\alpha}(z)", "Y_{\\alpha}(x)", "\\mathbf{M}_\\alpha(x)" ],
"isPartOf" : [ ],
"definiens" : [ ]
}