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List of all functions Maple supports
https://www.maplesoft.com/support/help/maple/view.aspx?path=initialfunction
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Collection of Mathematica functions
https://reference.wolfram.com/language/guide/MathematicalFunctions.html
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Compared with DLMF Macros (there are much more macros then Maple functions)
http://dlmf.nist.gov/&
hcohl/idllib/drmf/Glossary.csv
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Legend and Overview1)Elementary Functions&Generelaized Elementary Functions&Extras (basic functions)
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2)Special Functionsin Lexicographical Order
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3)Polynomialsin Lexicographical Order
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4)q-Hypergeometricin Lexicographical Order
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AttentionOwn Translation
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Differ in DefinitionNeed Additional Packages
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Issues:Fill Knowledge Gaps
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Columns for domain
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Discuss solutions for differences
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1)Elemntary Functions and their Generelized Companions
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Function ClassFunction NameDRMF MacroMaple FunctionMathematica FunctionMathematica-LinkMathematica CommentsMathematica Branch CutsDLMF-LinkMaplesoft-LinkComment
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Trigonometric FunctionsSine\sin@@{z}sin(z)Sin[$0]https://reference.wolfram.com/language/ref/Sin.htmlhttp://dlmf.nist.gov/4.14#E1https://www.maplesoft.com/support/help/maple/view.aspx?path=sin
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Cosine\cos@@{z}cos(z)Cos[$0]https://reference.wolfram.com/language/ref/Cos.htmlhttp://dlmf.nist.gov/4.14#E2https://www.maplesoft.com/support/help/maple/view.aspx?path=cos
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Tangent\tan@@{z}tan(z)Tan[$0]https://reference.wolfram.com/language/ref/Tan.htmlhttp://dlmf.nist.gov/4.14#E4https://www.maplesoft.com/support/help/maple/view.aspx?path=tan
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Secant\sec@@{z}sec(z)Sec[$0]https://reference.wolfram.com/language/ref/Sec.htmlhttp://dlmf.nist.gov/4.14#E6https://www.maplesoft.com/support/help/maple/view.aspx?path=sec
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Cosecant\csc@@{z}csc(z)Csc[$0]https://reference.wolfram.com/language/ref/Csc.htmlhttp://dlmf.nist.gov/4.14#E5https://www.maplesoft.com/support/help/maple/view.aspx?path=csc
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Cotangent\cot@@{z}cot(z)Cot[$0]https://reference.wolfram.com/language/ref/Cot.htmlhttp://dlmf.nist.gov/4.14#E7https://www.maplesoft.com/support/help/maple/view.aspx?path=cot
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Hyperbolic FunctionsHyperbolic sine\sinh@@{z}sinh(z)Sin[$0]https://reference.wolfram.com/language/ref/Sinh.htmlhttp://dlmf.nist.gov/4.28#E1https://www.maplesoft.com/support/help/maple/view.aspx?path=sinh
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Hyperbolic cosine\cosh@@{z}cosh(z)Cos[$0]https://reference.wolfram.com/language/ref/Cosh.htmlhttp://dlmf.nist.gov/4.28#E2https://www.maplesoft.com/support/help/maple/view.aspx?path=cosh
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Hyperbolic tangent\tanh@@{z}tanh(z)Tan[$0]https://reference.wolfram.com/language/ref/Tanh.htmlhttp://dlmf.nist.gov/4.28#E4https://www.maplesoft.com/support/help/maple/view.aspx?path=tanh
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Hyperbolic secant\sech@@{z}sech(z)Sec[$0]https://reference.wolfram.com/language/ref/Sech.htmlhttp://dlmf.nist.gov/4.28#E6https://www.maplesoft.com/support/help/maple/view.aspx?path=sech
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Hyperbolic cosecant\csch@@{z}csch(z)Csc[$0]https://reference.wolfram.com/language/ref/Csch.htmlhttp://dlmf.nist.gov/4.28#E5https://www.maplesoft.com/support/help/maple/view.aspx?path=csch
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Hyperbolic cotangent\coth@@{z}coth(z)Cot[$0]https://reference.wolfram.com/language/ref/Coth.htmlhttp://dlmf.nist.gov/4.28#E7https://www.maplesoft.com/support/help/maple/view.aspx?path=coth
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Inverse Trigonometric FunctionsInverse sine\asin@@{z}arcsin(z)ArcSin[$0]https://reference.wolfram.com/language/ref/ArcSin.htmlhttp://dlmf.nist.gov/4.23#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arcsin
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Inverse cosine\acos@@{z}arccos(z)ArcCos[$0]https://reference.wolfram.com/language/ref/ArcCos.htmlhttp://dlmf.nist.gov/4.23#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arccos
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Inverse tangent\atan@@{z}arctan(z)ArcTan[$0]https://reference.wolfram.com/language/ref/ArcTan.htmlhttp://dlmf.nist.gov/4.23#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arctan
For two-argument arctan(y,x) see Phase/Argument in this list
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Inverse secant\asec@@{z}arcsec(z)ArcSec[$0]https://reference.wolfram.com/language/ref/ArcSec.htmlhttp://dlmf.nist.gov/4.23#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arcsec
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Inverse cosecant\acsc@@{z}arccsc(z)ArcCsc[$0]https://reference.wolfram.com/language/ref/ArcCsc.htmlhttp://dlmf.nist.gov/4.23#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arccsc
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Inverse cotangent\acot@@{z}arccot(z)ArcCot[$0]https://reference.wolfram.com/language/ref/ArcCot.htmlhttp://dlmf.nist.gov/4.23#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arccot
Different branch cuts [Maple: (-i INF, -i), (i, i INF) / DLMF: (-i, i)]
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arctan(1/z)http://dlmf.nist.gov/4.23#E9
Use definition of Acot to avoid different branch cut
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I/2 * ln( (z-I)/(z+I) )http://dlmf.nist.gov/4.23#E26
Or use different definition to include z=0 (mentioned in Equation 25 in "According to Arbamowitz and Stegun or arccoth needn't be uncouth" by R.M. Corless, D.J. Jeffrey, S.M. Watt)
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Inverse Hyperbolic Trigonometric FunctionsInverse hyperbolic sine\asinh@@{z}arcsinh(z)ArcSinh[$0]https://reference.wolfram.com/language/ref/ArcSinh.htmlhttp://dlmf.nist.gov/4.37#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arcsinh
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Inverse hyperbolic cosine\acosh@@{z}arccosh(z)ArcCosh[$0]https://reference.wolfram.com/language/ref/ArcCosh.htmlhttp://dlmf.nist.gov/4.37#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arccosh
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Inverse hyperbolic tangent\atanh@@{z}arctanh(z)ArcTanh[$0]https://reference.wolfram.com/language/ref/ArcTanh.htmlhttp://dlmf.nist.gov/4.37#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arctanh
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Inverse hyperbolic secant\asech@@{z}arcsech(z)ArcSech[$0]https://reference.wolfram.com/language/ref/ArcSech.htmlhttp://dlmf.nist.gov/4.37#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arcsech
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Inverse hyperbolic cosecant\acsch@@{z}arccsch(z)ArcCsch[$0]https://reference.wolfram.com/language/ref/ArcCsch.htmlhttp://dlmf.nist.gov/4.37#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arccsch
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Inverse hyperbolic cotangent\acoth@@{z}arccoth(z)ArcCoth[$0]https://reference.wolfram.com/language/ref/ArcCoth.htmlhttp://dlmf.nist.gov/4.37#SS2.p1https://www.maplesoft.com/support/help/maple/view.aspx?path=arccoth
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Multivalued Inverse Trigonometric FunctionsInverse sine\Asin@@{z}http://dlmf.nist.gov/4.23#E1not defined
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Inverse cosine\Acos@@{z}http://dlmf.nist.gov/4.23#E2not defined
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Inverse tangent\Atan@@{z}http://dlmf.nist.gov/4.23#E3not defined
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Inverse secant\Asec@@{z}http://dlmf.nist.gov/4.23#E5not defined
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Inverse cosecant\Acsc@@{z}http://dlmf.nist.gov/4.23#E4not defined
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Inverse cotangent\Acot@@{z}http://dlmf.nist.gov/4.23#E6not defined
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Multivalued Inverse Hyperbolic Trigonometric FunctionsInverse hyperbolic sine\Asinh@@{z}http://dlmf.nist.gov/4.37#E1not defined
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Inverse hyperbolic cosine\Acosh@@{z}http://dlmf.nist.gov/4.37#E2not defined
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Inverse hyperbolic tangent\Atanh@@{z}http://dlmf.nist.gov/4.37#E3not defined
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Inverse hyperbolic secant\Asech@@{z}http://dlmf.nist.gov/4.37#E5not defined
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Inverse hyperbolic cosecant\Acsch@@{z}http://dlmf.nist.gov/4.37#E4not defined
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Inverse hyperbolic cotangent\Acoth@@{z}http://dlmf.nist.gov/4.37#E6not defined
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Logarithm and ExponentialNatural logarithm\ln@@{z}ln(z)Log[$0]https://reference.wolfram.com/language/ref/Log.htmlhttp://dlmf.nist.gov/4.2#E2https://www.maplesoft.com/support/help/maple/view.aspx?path=ln
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Natural logarithm\log@@{z}log(z)Log[$0]https://reference.wolfram.com/language/ref/Log.htmlhttp://dlmf.nist.gov/4.2#E2https://www.maplesoft.com/support/help/maple/view.aspx?path=logsame as ln
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Logarithm with different base\logb{a}@@{z}log[a](z)Log[$0,$1]https://reference.wolfram.com/language/ref/Log.htmlhttp://dlmf.nist.gov/4.2#EGx1https://www.maplesoft.com/support/help/maple/view.aspx?path=log
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Integer logarithmilog[b](x)not definedhttps://www.maplesoft.com/support/help/maple/view.aspx?path=ilogBased on IEEE function logb
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Multivalued logarithm\Ln@@{z}http://dlmf.nist.gov/4.2#E1not defined
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Exponential function\exp@@{z}exp(z)Exp[$0]https://reference.wolfram.com/language/ref/Exp.htmlhttp://dlmf.nist.gov/4.2#E19https://www.maplesoft.com/support/help/maple/view.aspx?path=exp
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Lambert W-FunctionsLambert W-Function\LambertW@{x}http://dlmf.nist.gov/4.13#p2https://www.maplesoft.com/support/help/maple/view.aspx?path=LambertWNeed a distinction of cases here.
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Lambert W-Function\LambertWp@{x}LambertW(x)ProductLog[$0]http://reference.wolfram.com/language/ref/ProductLog.htmlhttp://dlmf.nist.gov/4.13#p2https://www.maplesoft.com/support/help/maple/view.aspx?path=LambertW
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Lambert W-Function\LambertWm@{x}Re(LambertW(-1,x))ProductLog[-1, $0]http://reference.wolfram.com/language/ref/ProductLog.htmlhttp://dlmf.nist.gov/4.13#p2https://www.maplesoft.com/support/help/maple/view.aspx?path=LambertWonly for -1/e =< x < 0
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Sine and Cosine IntegralsSine integral\SinInt@{z}Si(z)SinIntegral[$0]https://reference.wolfram.com/language/ref/SinIntegral.htmlhttp://dlmf.nist.gov/6.2#E9https://www.maplesoft.com/support/help/maple/view.aspx?path=Si
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Shifted sine integral\sinInt@{z}Ssi(z)SinIntegral[$0] - Pi/2https://reference.wolfram.com/language/ref/SinIntegral.htmlhttp://dlmf.nist.gov/6.2#E10https://www.maplesoft.com/support/help/maple/view.aspx?path=Ssi
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Generalized sine integral\SinIntg@{a}{z}not definedhttp://dlmf.nist.gov/8.21#E2not defined
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Generalized sine integral\sinintg@{a}{z}not definedhttp://dlmf.nist.gov/8.21#E1not defined
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Cosine integral\CosInt@{z}Ci(z)CosIntegral[$0]https://reference.wolfram.com/language/ref/CosIntegral.htmlhttp://dlmf.nist.gov/6.2#E13https://www.maplesoft.com/support/help/maple/view.aspx?path=Ci
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Cosine integral\CosIntCin@{z}int((1-cos(t))/t, t = 0 .. z)not definedhttp://dlmf.nist.gov/6.2#E12not defined
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Generalized cosine integral\CosIntg@{a}{z}not definedhttp://dlmf.nist.gov/8.21#E2not defined
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Generalized cosine integral\cosintg@{a}{z}not definedhttp://dlmf.nist.gov/8.21#E1not defined
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Auxiliary function for sine and cosine integrals\SinCosIntf@{z}not definedhttp://dlmf.nist.gov/6.2#E17not defined
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Auxiliary function for sine and cosine integrals\SinCosIntg@{z}not definedhttp://dlmf.nist.gov/6.2#E18not defined
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Hyperbolic Sine and Cosine IntegralsHyperbolic sine integral\SinhInt@{z}Shi(z)SinhIntegral[$0]https://reference.wolfram.com/language/ref/SinhIntegral.htmlhttp://dlmf.nist.gov/6.2#E15https://www.maplesoft.com/support/help/maple/view.aspx?path=Shi
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Hyperbolic cosine integral\CoshInt@{z}Chi(z)CoshIntegral[$0]https://reference.wolfram.com/language/ref/CoshIntegral.htmlhttp://dlmf.nist.gov/6.2#E16https://www.maplesoft.com/support/help/maple/view.aspx?path=Chi
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Haversine FunctionHaversine function\sin{\frac{z}{2}}^2sin(z/2)^2Haversine[$0]https://reference.wolfram.com/language/ref/Haversine.htmlnot definednot defined
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Inverse Haversine function2 \asin{\sqrt{z}}2 arcsin(sqrt(z))InverseHaversine[$0]https://reference.wolfram.com/language/ref/InverseHaversine.htmlnot definednot defined
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Gudermannian FunctionGudermannian function\Gudermannian@@{x}int(sech(t), t = 0 .. x)Gudermannian[$0]https://reference.wolfram.com/language/ref/Gudermannian.htmlDefined also for imaginary values.http://dlmf.nist.gov/4.23#E39not defined
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Inverse Gudermannian function\arcGudermannian@@{x}int(sec(t), t = 0 .. x)InverseGudermannian[$0]https://reference.wolfram.com/language/ref/InverseGudermannian.htmlDefined also for imaginary values.http://dlmf.nist.gov/4.23#E41not defined
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Log and Exp IntegralsExponential integral\ExpInti@{x}Ei(x)-ExpIntegralEi[-($0)]https://reference.wolfram.com/language/ref/ExpIntegralEi.htmlMathematica uses another definition for the principle branch of the exponential integral. \ExpInti@{x} will be translated to -ExpIntegralEi[-x].http://dlmf.nist.gov/6.2#E1https://www.maplesoft.com/support/help/maple/view.aspx?path=Ei
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Exponential integral\ExpInt@{x}Ei(x)-ExpIntegralEi[-($0)]https://reference.wolfram.com/language/ref/ExpIntegralEi.htmlMathematica uses another definition for the principle branch of the exponential integral. \ExpInt@{x} will be translated to -ExpIntegralEi[-x].http://dlmf.nist.gov/6.2#E1https://www.maplesoft.com/support/help/maple/view.aspx?path=Ei
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Complementary exponential integral\ExpIntEin@{z}Ei(x)+ln(x)+gamma-ExpIntegralEi[-($0)] + Ln[$0] + EulerGammahttps://reference.wolfram.com/language/ref/ExpIntegralEi.htmlThe translation based on the definition in DLMF.http://dlmf.nist.gov/6.2#E3not defined
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Generalized exponential integral\ExpIntn{p}@{z}Ei(p, z)http://dlmf.nist.gov/8.19#E1https://www.maplesoft.com/support/help/maple/view.aspx?path=Ei
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