# SpheroidalJoiningFactor

SpheroidalJoiningFactor[n,m,γ]

gives the spheroidal joining factor with degree and order .

# Examples

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## 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:

### 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 and generic values of :

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 ]}