- Mathematical function, suitable for both symbolic and numerical manipulation.
- The satisfy the recurrence relation with , .
- For any complex value of n the are given by the general formula , where is the golden ratio.
- The Lucas polynomial is the coefficient of in the expansion of .
- The Lucas polynomials satisfy the recurrence relation .
- LucasL can be evaluated to arbitrary numerical precision.
- LucasL automatically threads over lists.
Examplesopen allclose all
Basic Examples (4)
Numerical Evaluation (4)
Specific Values (6)
Function Properties (14)
LucasL is defined for all real and complex values:
LucasL has the mirror property :
LucasL threads elementwise over lists:
LucasL is neither non-decreasing nor non-increasing for even values:
LucasL is non-decreasing for odd values:
LucasL is not injective for even values:
LucasL is not surjective for even values:
LucasL is non-negative for even values:
LucasL does not have singularity nor discontinuity:
LucasL is convex for even values:
Series Expansions (4)
Function Identities and Simplifications (2)
The ordinary generating function of LucasL:
Properties & Relations (10)
General term in the series expansion of LucasL:
The generating function for LucasL:
The exponential generating function for LucasL:
Possible Issues (2)
Wolfram Research (2007), LucasL, Wolfram Language function, https://reference.wolfram.com/language/ref/LucasL.html (updated 2008).
Wolfram Language. 2007. "LucasL." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/LucasL.html.
Wolfram Language. (2007). LucasL. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LucasL.html