({{, (RefLink[EllipticExpPrime, paclet:ref/EllipticExpPrime])[u,{a,b}] 
gives the derivative of (RefLink[EllipticExp, paclet:ref/EllipticExp])[u,{a,b}] with respect to u.}})

OpenersNotesSection(Spacer1)Details

Mathematical function, suitable for both symbolic and numerical manipulation.

For certain special arguments, (RefLink[EllipticExpPrime, paclet:ref/EllipticExpPrime]) automatically evaluates to exact values.

(RefLink[EllipticExpPrime, paclet:ref/EllipticExpPrime]) can be evaluated to arbitrary numerical precision.

OpenersPrimaryExamplesSection(Spacer1)Examples  (13)

OpenersExampleSection0(Spacer1)Basic Examples  (2)

Evaluate numerically:

EllipticExpPrime[-0.4, {4., 1}]

Plot[Re[EllipticExpPrime[x, {4, 1}]],{x,-5,5}]

OpenersExampleSection1(Spacer1)Scope  (9)

OpenersExampleSubsection0(Spacer1)Numerical Evaluation  (4)

Evaluate numerically:

EllipticExpPrime[6.,{4,1}]

EllipticExpPrime[-.2,{3,2}]

Evaluate to high precision:

N[EllipticExpPrime[1/3,{5,1}],50]

The precision of the output tracks the precision of the input:

EllipticExpPrime[0.3333330003333333333,{5,1}]

Complex number inputs:

N[EllipticExpPrime[27+I,{5-I,2}]]

Evaluate efficiently at high precision:

N[EllipticExpPrime[157`10,{5,1}],50]//Timing

N[EllipticExpPrime[157`10000,{5,1}],50];//Timing

OpenersExampleSubsection1(Spacer1)Specific Values   (2)

Values at fixed points:

Table[EllipticExpPrime[x,{0 ,0}],{x,{-1,2}}]

Value at zero:

EllipticExpPrime[0,{1,2}]

OpenersExampleSubsection2(Spacer1)Visualization  (2)

Plot the (RefLink[EllipticExpPrime, paclet:ref/EllipticExpPrime]) function for various parameters:

Plot[{EllipticExpPrime[u,{2,3}],EllipticExpPrime[u,{4,3}],EllipticExpPrime[-u,{4,3}]},{u,-3,3}]

Plot the real part of EllipticExpPrime[x+i y,{1,2}]:

ContourPlot[Re[EllipticExpPrime[x+I y,{1,2}]],{x,-3,3},{y,-3,3},Contours->24]

Plot the imaginary part of EllipticExpPrime[x+i y,{1,2}]:

ContourPlot[Im[EllipticExpPrime[x+I y,{1,2}]],{x,-3,3},{y,-3,3},Contours->24]

OpenersExampleSubsection3(Spacer1)Integration  (1)

Compute the indefinite integral using (RefLink[Integrate, paclet:ref/Integrate]):

Integrate[EllipticExpPrime[u,{a,b}],u]

Verify the anti-derivative:

FullSimplify[D[%,u]]

OpenersExampleSection2(Spacer1)Applications  (1)

Visualize the function:

Plot3D[Norm[EllipticExpPrime[x+I y, {1, 2}]],{x,-3,3},{y,-3,3}]

OpenersExampleSection3(Spacer1)Properties & Relations  (1)

(RefLink[EllipticExpPrime, paclet:ref/EllipticExpPrime]) is the derivative of (RefLink[EllipticExp, paclet:ref/EllipticExp]):

D[EllipticExp[u,{a,b}],u]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[EllipticExp, paclet:ref/EllipticExp])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Elliptic Functions, paclet:guide/EllipticFunctions])}})}})