SpheroidalRadialFactor

SpheroidalRadialFactor[n,m,c]

gives the spheroidal radial factor with degree n and order m.

Details

Examples

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Basic Examples  (2)

Evaluate numerically:

Plot over a subset of the reals:

Scope  (11)

Numerical Evaluation  (4)

Evaluate numerically:

Evaluate to high precision:

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

Complex number inputs:

Evaluate efficiently at high precision:

Specific Values  (2)

Value at zero:

Find the first positive maximum of SpheroidalRadialFactor[3,2,x]:

Visualization  (2)

Plot the SpheroidalRadialFactor function:

Plot the real part of SpheroidalRadialFactor[2,1,x+ y]:

Plot the imaginary part of SpheroidalRadialFactor[2,1,x+ y]:

Function Properties  (3)

has no singularities or discontinuities:

is neither nondecreasing nor nonincreasing:

is neither convex nor concave:

Applications  (1)

Build a near-spherical approximation to :

First few terms of the approximation:

Compare numerically:

Wolfram Research (2007), SpheroidalRadialFactor, Wolfram Language function, https://reference.wolfram.com/language/ref/SpheroidalRadialFactor.html.

Text

Wolfram Research (2007), SpheroidalRadialFactor, Wolfram Language function, https://reference.wolfram.com/language/ref/SpheroidalRadialFactor.html.

CMS

Wolfram Language. 2007. "SpheroidalRadialFactor." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SpheroidalRadialFactor.html.

APA

Wolfram Language. (2007). SpheroidalRadialFactor. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SpheroidalRadialFactor.html

BibTeX

@misc{reference.wolfram_2025_spheroidalradialfactor, author="Wolfram Research", title="{SpheroidalRadialFactor}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/SpheroidalRadialFactor.html}", note=[Accessed: 02-August-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_spheroidalradialfactor, organization={Wolfram Research}, title={SpheroidalRadialFactor}, year={2007}, url={https://reference.wolfram.com/language/ref/SpheroidalRadialFactor.html}, note=[Accessed: 02-August-2025 ]}