1
2
List of all functions Maple supports
https://www.maplesoft.com/support/help/maple/view.aspx?path=initialfunction
3
Collection of Mathematica functions
https://reference.wolfram.com/language/guide/MathematicalFunctions.html
4
Compared with DLMF Macros (there are much more macros then Maple functions)
http://dlmf.nist.gov/&
hcohl/idllib/drmf/Glossary.csv
5
6
Legend and Overview1)Elementary Functions&Generelaized Elementary Functions&Extras (basic functions)
7
2)Special Functionsin Lexicographical Order
8
3)Polynomialsin Lexicographical Order
9
4)q-Hypergeometricin Lexicographical Order
10
11
AttentionOwn Translation
12
13
Differ in DefinitionNeed Additional Packages
14
15
Issues:Fill Knowledge Gaps
16
Columns for domain
17
Discuss solutions for differences
18
19
20
1)Elemntary Functions and their Generelized Companions
21
22
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 23 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
24
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 25 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
26
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 27 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
28
29
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 30 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
31
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 32 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
33
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 34 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
35
36
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 37 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
38
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 39 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
40
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 41 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)]
42
arctan(1/z)http://dlmf.nist.gov/4.23#E9
Use definition of Acot to avoid different branch cut
43
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)
44
45
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 46 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
47
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 48 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
49
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 50 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
51
52
Multivalued Inverse Trigonometric FunctionsInverse sine\Asin@@{z}http://dlmf.nist.gov/4.23#E1not defined
53
Inverse cosine\Acos@@{z}http://dlmf.nist.gov/4.23#E2not defined
54
Inverse tangent\Atan@@{z}http://dlmf.nist.gov/4.23#E3not defined
55
Inverse secant\Asec@@{z}http://dlmf.nist.gov/4.23#E5not defined
56
Inverse cosecant\Acsc@@{z}http://dlmf.nist.gov/4.23#E4not defined
57
Inverse cotangent\Acot@@{z}http://dlmf.nist.gov/4.23#E6not defined
58
59
Multivalued Inverse Hyperbolic Trigonometric FunctionsInverse hyperbolic sine\Asinh@@{z}http://dlmf.nist.gov/4.37#E1not defined
60
Inverse hyperbolic cosine\Acosh@@{z}http://dlmf.nist.gov/4.37#E2not defined
61
Inverse hyperbolic tangent\Atanh@@{z}http://dlmf.nist.gov/4.37#E3not defined
62
Inverse hyperbolic secant\Asech@@{z}http://dlmf.nist.gov/4.37#E5not defined
63
Inverse hyperbolic cosecant\Acsch@@{z}http://dlmf.nist.gov/4.37#E4not defined
64
Inverse hyperbolic cotangent\Acoth@@{z}http://dlmf.nist.gov/4.37#E6not defined
65
66
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 67 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
68
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
69
Integer logarithmilog[b](x)not definedhttps://www.maplesoft.com/support/help/maple/view.aspx?path=ilogBased on IEEE function logb
70
Multivalued logarithm\Ln@@{z}http://dlmf.nist.gov/4.2#E1not defined
71
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 72 73 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. 74 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
75
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 76 77 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
78
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 79 Generalized sine integral\SinIntg@{a}{z}not definedhttp://dlmf.nist.gov/8.21#E2not defined 80 Generalized sine integral\sinintg@{a}{z}not definedhttp://dlmf.nist.gov/8.21#E1not defined 81 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
82
Cosine integral\CosIntCin@{z}int((1-cos(t))/t, t = 0 .. z)not definedhttp://dlmf.nist.gov/6.2#E12not defined
83
Generalized cosine integral\CosIntg@{a}{z}not definedhttp://dlmf.nist.gov/8.21#E2not defined
84
Generalized cosine integral\cosintg@{a}{z}not definedhttp://dlmf.nist.gov/8.21#E1not defined
85
Auxiliary function for sine and cosine integrals\SinCosIntf@{z}not definedhttp://dlmf.nist.gov/6.2#E17not defined
86
Auxiliary function for sine and cosine integrals\SinCosIntg@{z}not definedhttp://dlmf.nist.gov/6.2#E18not defined
87
88
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 89 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
90
91
Haversine FunctionHaversine function\sin{\frac{z}{2}}^2sin(z/2)^2Haversine[$0]https://reference.wolfram.com/language/ref/Haversine.htmlnot definednot defined 92 Inverse Haversine function2 \asin{\sqrt{z}}2 arcsin(sqrt(z))InverseHaversine[$0]https://reference.wolfram.com/language/ref/InverseHaversine.htmlnot definednot defined
93
94
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 95 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
96
97
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 98 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
99
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
100
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