LameC
✖
LameC
Details
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- LameC belongs to the Lamé class of functions and solves boundary-value problems for Laplace's equation in ellipsoidal and spheroconal coordinates, as well as occurring in other problems of mathematical physics and quantum mechanics.
- Mathematical function, suitable for both symbolic and numerical manipulation.
- LameC[ν,j,z,m] satisfies the Lamé differential equation
, with the Lamé eigenvalue
given by LameEigenvalueA[ν,j,m], and where
is the Jacobi elliptic function JacobiSN[z,m].
- For certain special arguments, LameC automatically evaluates to exact values.
- LameC can be evaluated to arbitrary numerical precision for an arbitrary complex argument.
- LameC automatically threads over lists.
- LameC[ν,0,z,0]=
and LameC[ν,j,z,0]=Cos[j(
-z)].
- LameC[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)Summary of the most common use cases
Scope (27)Survey of the scope of standard use cases
Numerical Evaluation (5)
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https://wolfram.com/xid/0wgtmv5-okwtpc
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The precision of the output tracks the precision of the input:
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https://wolfram.com/xid/0wgtmv5-kkvikx
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LameC can take complex number parameters and argument:
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https://wolfram.com/xid/0wgtmv5-hqtw40
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https://wolfram.com/xid/0wgtmv5-zgyi26
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Evaluate LameC efficiently at high precision:
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https://wolfram.com/xid/0wgtmv5-qn20jy
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https://wolfram.com/xid/0wgtmv5-jlo2be
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https://wolfram.com/xid/0wgtmv5-clqbry
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https://wolfram.com/xid/0wgtmv5-dhyb88
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https://wolfram.com/xid/0wgtmv5-h6iizh
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Specific Values (3)
Value of LameC when and
:
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https://wolfram.com/xid/0wgtmv5-vlsc9t
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Value of LameC when and
:
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https://wolfram.com/xid/0wgtmv5-i8zbem
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Some poles of LameC:
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https://wolfram.com/xid/0wgtmv5-6x592
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For integer values of and
, LameC can be expressed entirely in terms of Jacobi elliptic functions:
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https://wolfram.com/xid/0wgtmv5-by033o
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https://wolfram.com/xid/0wgtmv5-5h6j9
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Visualization (6)
Plot the first three even LameC functions:
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https://wolfram.com/xid/0wgtmv5-2nkt2z
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Plot the first three odd LameC functions:
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https://wolfram.com/xid/0wgtmv5-eezd2
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Plot the absolute value of the LameC function for complex parameters:
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https://wolfram.com/xid/0wgtmv5-cv7enz
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Plot LameC as a function of its first parameter :
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https://wolfram.com/xid/0wgtmv5-0oazxn
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Plot LameC as a function of and elliptic parameter
:
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https://wolfram.com/xid/0wgtmv5-kavekp
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Plot the family of LameC functions for different values of the elliptic parameter :
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https://wolfram.com/xid/0wgtmv5-m5b5wf
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Function Properties (2)
When is even, LameC is a periodic function of real argument
with a period 2EllipticK[m]:
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https://wolfram.com/xid/0wgtmv5-20emv
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https://wolfram.com/xid/0wgtmv5-pbglku
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When is odd, LameC is a periodic function of real argument
with a period 4EllipticK[m] and has an initial value LameC[ν,j,0,m]=0:
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https://wolfram.com/xid/0wgtmv5-m4hob1
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https://wolfram.com/xid/0wgtmv5-hvapl9
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Differentiation (3)
The -derivative of LameC is LameCPrime:
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https://wolfram.com/xid/0wgtmv5-6eb2k6
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Higher derivatives of LameC are calculated using LameCPrime:
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https://wolfram.com/xid/0wgtmv5-baz2gr
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Derivatives of LameC for specific cases of parameters:
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https://wolfram.com/xid/0wgtmv5-6je6g8
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https://wolfram.com/xid/0wgtmv5-yw3970
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Integration (3)
Indefinite integrals of LameC cannot be expressed in elementary or other special functions:
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https://wolfram.com/xid/0wgtmv5-ecaem6
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Definite numerical integrals of LameC:
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https://wolfram.com/xid/0wgtmv5-yy7qm6
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More integrals with LameC:
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https://wolfram.com/xid/0wgtmv5-77lshe
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https://wolfram.com/xid/0wgtmv5-d5fnzu
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Series Expansions (3)
Series expansion of LameC at the origin:
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https://wolfram.com/xid/0wgtmv5-0rpbb6
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Coefficient of the second-order term of this expansion:
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https://wolfram.com/xid/0wgtmv5-9rxgh1
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Plot the first- and third-order approximations for LameC around :
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https://wolfram.com/xid/0wgtmv5-zgnxgy
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https://wolfram.com/xid/0wgtmv5-jch4ka
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https://wolfram.com/xid/0wgtmv5-hrtnwe
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Series expansion for LameC at any ordinary complex point:
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https://wolfram.com/xid/0wgtmv5-ukhgue
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Function Representations (2)
LameC cannot be represented in terms of MeijerG:
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https://wolfram.com/xid/0wgtmv5-bfvi7o
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TraditionalForm formatting:
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https://wolfram.com/xid/0wgtmv5-ha9m21
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Applications (1)Sample problems that can be solved with this function
LameC solves the Lamé differential equation when h=LameEigenvalueA[ν,j,m]:
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https://wolfram.com/xid/0wgtmv5-nkp6ld
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https://wolfram.com/xid/0wgtmv5-8yj5vx
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Properties & Relations (2)Properties of the function, and connections to other functions
LameC is an even function when is a non-negative even integer:
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https://wolfram.com/xid/0wgtmv5-2dos
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LameC is an odd function when is a positive odd integer:
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https://wolfram.com/xid/0wgtmv5-1317ex
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Use FunctionExpand to expand LameC for integer values of and
:
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https://wolfram.com/xid/0wgtmv5-bxtg9f
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Wolfram Research (2020), LameC, Wolfram Language function, https://reference.wolfram.com/language/ref/LameC.html.
Text
Wolfram Research (2020), LameC, Wolfram Language function, https://reference.wolfram.com/language/ref/LameC.html.
Wolfram Research (2020), LameC, Wolfram Language function, https://reference.wolfram.com/language/ref/LameC.html.
CMS
Wolfram Language. 2020. "LameC." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LameC.html.
Wolfram Language. 2020. "LameC." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LameC.html.
APA
Wolfram Language. (2020). LameC. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LameC.html
Wolfram Language. (2020). LameC. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LameC.html
BibTeX
@misc{reference.wolfram_2025_lamec, author="Wolfram Research", title="{LameC}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/LameC.html}", note=[Accessed: 24-February-2025
]}
BibLaTeX
@online{reference.wolfram_2025_lamec, organization={Wolfram Research}, title={LameC}, year={2020}, url={https://reference.wolfram.com/language/ref/LameC.html}, note=[Accessed: 24-February-2025
]}