SpheroidalJoiningFactor

SpheroidalJoiningFactor[n,m,γ]

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

Details

Examples

open allclose all

Basic Examples  (2)

Evaluate numerically:

Plot over a subset of the reals:

Scope  (9)

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  (3)

Value at zero:

Find a value of x for which SpheroidalJoiningFactor[0,1/2,x]=5:

SpheroidalJoiningFactor threads elementwise over lists:

Visualization  (2)

Plot the SpheroidalJoiningFactor function:

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

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

Applications  (1)

A relation between radial and angular spheroidal functions:

Check numerically:

Possible Issues  (1)

Spheroidal functions do not evaluate for half-integer values of n and generic values of m:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2022_spheroidaljoiningfactor, author="Wolfram Research", title="{SpheroidalJoiningFactor}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/SpheroidalJoiningFactor.html}", note=[Accessed: 01-June-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_spheroidaljoiningfactor, organization={Wolfram Research}, title={SpheroidalJoiningFactor}, year={2007}, url={https://reference.wolfram.com/language/ref/SpheroidalJoiningFactor.html}, note=[Accessed: 01-June-2023 ]}