# 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.
• ScorerHi can be used with Interval and CenteredInterval objects. »

# 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(32)

### Numerical Evaluation(6)

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:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix ScorerHi function using MatrixFunction:

### 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 :

Plot the imaginary part of :

### Function Properties(11)

Real domain of ScorerHi:

Complex domain:

Approximate function range of ScorerHi:

ScorerHi is an analytic function of x:

ScorerHi is nondecreasing:

ScorerHi is injective:

ScorerHi is not surjective:

ScorerHi is non-negative:

ScorerHi does not have either singularity or discontinuity:

ScorerHi is convex:

### Differentiation and Integration(5)

First derivative with respect to z:

Higher derivatives with respect to z:

Plot the higher derivatives with respect to z:

Formula for the derivative with respect to z:

Indefinite integral of ScorerHi:

More integrals:

### 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(3)

FunctionExpand tries to simplify the argument of ScorerHi:

Functional identity:

ScorerHi can be represented as a DifferentialRoot:

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.

#### 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

#### BibTeX

@misc{reference.wolfram_2024_scorerhi, author="Wolfram Research", title="{ScorerHi}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/ScorerHi.html}", note=[Accessed: 13-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_scorerhi, organization={Wolfram Research}, title={ScorerHi}, year={2014}, url={https://reference.wolfram.com/language/ref/ScorerHi.html}, note=[Accessed: 13-September-2024 ]}