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LameEigenvalueA[ν,j,m]

gives the ^(th) Lamé eigenvalue TemplateBox[{nu, j, m}, LameEigenvalueA] of order with elliptic parameter for the function LameC[ν,j,z,m].

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Numerical Evaluation  
Specific Values  
Visualization  
Series Expansions  
Function Representations  
Applications  
Properties & Relations  
Possible Issues  
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Related Guides
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LameEigenvalueA

LameEigenvalueA[ν,j,m]

gives the ^(th) Lamé eigenvalue TemplateBox[{nu, j, m}, LameEigenvalueA] of order with elliptic parameter for the function LameC[ν,j,z,m].

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The Lamé eigenvalue TemplateBox[{nu, j, m}, LameEigenvalueA] for successive gives the value of the parameter in the Lamé differential equation (where TemplateBox[{z, m}, JacobiSN] is the Jacobi elliptic function JacobiSN[z,m]), for which the solution is the function LameC[ν,j,z,m].
  • For certain special arguments, LameEigenvalueA automatically evaluates to exact values.
  • LameEigenvalueA[ν,j,0]=j2.
  • LameEigenvalueA can be evaluated to arbitrary numerical precision.
  • LameEigenvalueA automatically threads over lists.

Examples

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Basic Examples  (2)

Evaluate numerically:

Wolfram Language code: LameEigenvalueA[0.9, 2, 0.3]

Plot the LameEigenvalueA function:

Wolfram Language code: Plot[LameEigenvalueA[ν, 2, 0.5], {ν, -1 / 2, 6}]

Scope  (14)

Numerical Evaluation  (5)

Evaluate to high precision:

Wolfram Language code: N[LameEigenvalueA[9 / 10, 2, 3 / 10], 50]

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

Wolfram Language code: LameEigenvalueA[9 / 10, 2, 0.33333333333333333333331]

LameEigenvalueA can take complex number parameters and argument:

Wolfram Language code: LameEigenvalueA[1.2 + I, 2, 0.3]
Wolfram Language code: LameEigenvalueA[1.2 + I, 2, 0.3 + I]

Evaluate LameEigenvalueA efficiently at high precision:

Wolfram Language code: LameEigenvalueA[0.9, 2, 3 / 10`500]//Timing
Wolfram Language code: LameEigenvalueA[0.9, 2, 3 / 10`500 + I]//Timing

Lists and matrices:

Wolfram Language code: LameEigenvalueA[0.9, 2, {0.1, 0.1 + I, I, 4}]
Wolfram Language code: LameEigenvalueA[0.9, 2, (| | | | :- | :---- | | π | u | | v | (π/2) |)]

Specific Values  (2)

Value of LameEigenvalueA when and :

Wolfram Language code: LameEigenvalueA[ν, 0, 0]

Value of LameEigenvalueA for and is :

Wolfram Language code: LameEigenvalueA[0, 5, 0]

For integer values of and , LameEigenvalueA is the root of a polynomial:

Wolfram Language code: LameEigenvalueA[3, 0, (1/2)]//FunctionExpand
Wolfram Language code: LameEigenvalueA[4, 2, (1/2)]//FunctionExpand

Visualization  (5)

Plot the first five LameEigenvalueA functions:

Wolfram Language code: Plot[Evaluate[Table[LameEigenvalueA[3 / 2, j, m], {j, 0, 4}]], {m, 0, 1}]

Plot the absolute value of the LameEigenvalueA function for complex :

Wolfram Language code: Plot[Abs[LameEigenvalueA[3 / 2 + I, 3, m]], {m, 0, 1}]

Plot LameEigenvalueA as a function of its first parameter :

Wolfram Language code: Plot[{LameEigenvalueA[-1 / 2, 2, m], LameEigenvalueA[2, 2, m], LameEigenvalueA[3, 2, m]}, {m, 0, 1}]

Plot LameEigenvalueA as a function of order and elliptic parameter :

Wolfram Language code: Plot3D[LameEigenvalueA[ν, 1, m], {ν, -1 / 2, 1}, {m, 0, 1}]

Plot the family of LameEigenvalueA functions for different values of the elliptic parameter :

Wolfram Language code: Plot[Evaluate[Table[LameEigenvalueA[ν, 2, m], {m, 0, 1, 1 / 15}]], {ν, -1 / 2, 4}, PlotStyle -> Table[{Hue[i / 20], Thickness[0.002]}, {i, 20}], PlotRange -> All, Frame -> True, Axes -> False]

Series Expansions  (1)

Series expansion of LameEigenvalueA with at :

Wolfram Language code: Series[LameEigenvalueA[ν, 0, m], {m, 0, 4}]

Series expansion of LameEigenvalueA with at :

Wolfram Language code: Series[LameEigenvalueA[ν, 3, m], {m, 0, 4}]

Function Representations  (1)

TraditionalForm formatting:

Wolfram Language code: LameEigenvalueA[ν, j, m]//TraditionalForm

Applications  (1)

LameC solves the Lamé differential equation only if the parameter is specialized to LameEigenvalueA:

Wolfram Language code: y[x_] := LameC[ν, j, x, m];
Wolfram Language code: y''[x] + (LameEigenvalueA[ν, j, m] - ν(ν + 1)m JacobiSN[x, m]^2)y[x] == 0//Simplify

Properties & Relations  (2)

Use FunctionExpand to expand LameEigenvalueA for integer values of and :

Wolfram Language code: LameEigenvalueA[7, 5, (3/4)]//FunctionExpand

LameEigenvalueA satisfies a symmetry relation for integer values of and and :

Wolfram Language code: With[{n = 8, j = 5, m = 1 / 2}, LameEigenvalueA[n, j, m] + LameEigenvalueA[n, n - j, 1 - m] - n(n + 1)//FunctionExpand//FullSimplify]

Possible Issues  (1)

LameEigenvalueA is not defined if is a negative integer:

Wolfram Language code: LameEigenvalueA[ν, -3, m]

LameEigenvalueA is not defined if is not an integer:

Wolfram Language code: LameEigenvalueA[ν, 3 / 2, m]
Wolfram Research (2020), LameEigenvalueA, Wolfram Language function, https://reference.wolfram.com/language/ref/LameEigenvalueA.html.

Text

Wolfram Research (2020), LameEigenvalueA, Wolfram Language function, https://reference.wolfram.com/language/ref/LameEigenvalueA.html.

CMS

Wolfram Language. 2020. "LameEigenvalueA." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LameEigenvalueA.html.

APA

Wolfram Language. (2020). LameEigenvalueA. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LameEigenvalueA.html

BibTeX

@misc{reference.wolfram_2026_lameeigenvaluea, author="Wolfram Research", title="{LameEigenvalueA}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/LameEigenvalueA.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_lameeigenvaluea, organization={Wolfram Research}, title={LameEigenvalueA}, year={2020}, url={https://reference.wolfram.com/language/ref/LameEigenvalueA.html}, note=[Accessed: 12-June-2026]}