ScorerHi

ScorerHi[z]

gives the Scorer function .

Details

  • ScorerHi is also known as an inhomogeneous Airy function.
  • Mathematical function, suitable for both symbolic and numeric manipulation.
  • The Scorer function is a solution to the inhomogeneous Airy differential equation .
  • tends to zero as .
  • ScorerHi[z] is an entire function of z with no branch cut discontinuities.
  • For certain arguments, ScorerHi automatically evaluates to exact values.
  • ScorerHi can be evaluated to arbitrary numerical precision.
  • ScorerHi automatically threads over lists.

Examples

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Basic Examples  (4)

Evaluate numerically:

Plot over a subset of the reals:

Plot over a subset of the complexes:

Series expansion at the origin:

Scope  (27)

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)

Simple exact values are generated automatically:

Limiting values at infinity:

Find a value of x for which ScorerHi[x]=4:

Visualization  (2)

Plot the ScorerHi function:

Plot the real part of TemplateBox[{{x, +, ⅈy}}, ScorerHi]:

Plot the imaginary part of TemplateBox[{{x, +, ⅈy}}, ScorerHi]:

Function Properties  (11)

Real domain of ScorerHi:

Complex domain:

Approximate function range of ScorerHi:

ScorerHi threads elementwise over lists:

ScorerHi is an analytic function of x:

ScorerHi is non-decreasing:

ScorerHi is injective:

ScorerHi is not surjective:

ScorerHi is non-negative:

ScorerHi does not have either singularity or discontinuity:

ScorerHi is convex:

TraditionalForm typesetting:

Differentiation  (3)

First derivative with respect to z:

Higher derivatives with respect to z:

Plot the higher derivatives with respect to z:

Formula for the ^(th) derivative with respect to z:

Series Expansions  (2)

Find the Taylor expansion using Series:

Plots of the first three approximations around :

Taylor expansion at a generic point:

Function Identities and Simplifications  (2)

FunctionExpand tries to simplify the argument of ScorerHi:

Functional identity:

Wolfram Research (2014), ScorerHi, Wolfram Language function, https://reference.wolfram.com/language/ref/ScorerHi.html.

Text

Wolfram Research (2014), ScorerHi, Wolfram Language function, https://reference.wolfram.com/language/ref/ScorerHi.html.

BibTeX

@misc{reference.wolfram_2021_scorerhi, author="Wolfram Research", title="{ScorerHi}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/ScorerHi.html}", note=[Accessed: 22-October-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_scorerhi, organization={Wolfram Research}, title={ScorerHi}, year={2014}, url={https://reference.wolfram.com/language/ref/ScorerHi.html}, note=[Accessed: 22-October-2021 ]}

CMS

Wolfram Language. 2014. "ScorerHi." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ScorerHi.html.

APA

Wolfram Language. (2014). ScorerHi. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ScorerHi.html