LameS
LameS[ν,j,z,m]
gives the Lamé function
of order
with elliptic parameter
.
Details

- LameS belongs to the Lamé class of functions and solves boundary-value problems for Laplace's equation in ellipsoidal and spheroconal coordinates and also occurs in other problems of mathematical physics and quantum mechanics.
- Mathematical function, suitable for both symbolic and numerical manipulation.
- LameS[ν,j,z,m] satisfies the Lamé differential equation
, with the Lamé eigenvalue
given by LameEigenvalueB[ν,j,m], and where
is the Jacobi elliptic function JacobiSN[z,m].
- For certain special arguments, LameS automatically evaluates to exact values.
- LameS can be evaluated to arbitrary numerical precision for arbitrary complex argument.
- LameS automatically threads over lists.
- LameS[ν,j,z,0]=Sin[j(
-z)].
- LameS[ν,j,z,m] is proportional to HeunG[a,q,α,β,γ,δ,ξ], where
, if the parameters of HeunG are specialized as follows:
.
Examples
open allclose allBasic Examples (3)
Scope (24)
Numerical Evaluation (5)
Visualization (6)
Plot the first three even LameS functions:
Plot the first three odd LameS functions:
Plot the absolute value of the LameS function for complex parameters:
Plot LameS as a function of its first parameter :
Plot LameS as a function of and elliptic parameter
:
Plot the family of LameS functions for different values of the elliptic parameter :
Function Properties (2)
Differentiation (3)
The -derivative of LameS is LameSPrime:
Higher derivatives of LameS are calculated using LameSPrime:
Derivatives of LameS for specific cases of parameters:
Integration (3)
Series Expansions (3)
Applications (1)
LameS solves the Lamé differential equation when h=LameEigenvalueB[ν,j,m]:
Properties & Relations (1)
Text
Wolfram Research (2020), LameS, Wolfram Language function, https://reference.wolfram.com/language/ref/LameS.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 2020. "LameS." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LameS.html.
APA
Wolfram Language. (2020). LameS. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LameS.html