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:

Plot the LameEigenvalueA function:

Scope  (14)

Numerical Evaluation  (5)

Evaluate to high precision:

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

LameEigenvalueA can take complex number parameters and argument:

Evaluate LameEigenvalueA efficiently at high precision:

Lists and matrices:

Specific Values  (2)

Value of LameEigenvalueA when and :

Value of LameEigenvalueA for and is :

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

Visualization  (5)

Plot the first five LameEigenvalueA functions:

Plot the absolute value of the LameEigenvalueA function for complex :

Plot LameEigenvalueA as a function of its first parameter :

Plot LameEigenvalueA as a function of order and elliptic parameter :

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

Series Expansions  (1)

Series expansion of LameEigenvalueA with at :

Series expansion of LameEigenvalueA with at :

Function Representations  (1)

TraditionalForm formatting:

Applications  (1)

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

Properties & Relations  (2)

Use FunctionExpand to expand LameEigenvalueA for integer values of and :

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

Possible Issues  (1)

LameEigenvalueA is not defined if is a negative integer:

LameEigenvalueA is not defined if is not an integer:

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_2024_lameeigenvaluea, author="Wolfram Research", title="{LameEigenvalueA}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/LameEigenvalueA.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_lameeigenvaluea, organization={Wolfram Research}, title={LameEigenvalueA}, year={2020}, url={https://reference.wolfram.com/language/ref/LameEigenvalueA.html}, note=[Accessed: 21-December-2024 ]}