Package org.drip.specialfunction.digamma

Class CumulativeSeriesEstimator

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.R1ToR1Estimator

org.drip.specialfunction.digamma.CumulativeSeriesEstimator

public abstract class CumulativeSeriesEstimator
extends R1ToR1Estimator

CumulativeSeriesEstimator implements the Cumulative Series Based Digamma Estimation. The References are:

• Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
• Blagouchine, I. V. (2018): Three Notes on Ser's and Hasse's Representations for the Zeta-Functions https://arxiv.org/abs/1606.02044 arXiv
• Mezo, I., and M. E. Hoffman (2017): Zeros of the Digamma Function and its Barnes G-function Analogue Integral Transforms and Special Functions 28 (28) 846-858
• Whitaker, E. T., and G. N. Watson (1996): A Course on Modern Analysis Cambridge University Press New York
• Wikipedia (2019): Digamma Function https://en.wikipedia.org/wiki/Digamma_function

It provides the following functionality:

• Compute the Abramowitz-Stegun (2007) Cumulative Series of Digamma Estimator
• Compute the Harmonic Cumulative Series of Digamma Estimator
• Compute the Half-Integer Cumulative Series of Digamma Estimator
• Compute the Saddle-Point Cumulative Series of Digamma Estimator
• Compute the Gauss Cumulative Series of Digamma Estimator
• Compute the Asymptotic Cumulative Series of Digamma Estimator
• Compute the Exponential Asymptotic Cumulative Series of Digamma Estimator
• Compute the Exponential Asymptotic Cumulative Series of Digamma + 0.5 Estimator
• Compute the Taylor-Riemann Zeta Cumulative Series of Digamma Estimator
• Retrieve the Underlying Cumulative Series

Module	Product Core Module
Library	Fixed Income Analytics
Project	Special Function Implementation and Analysis
Package	Estimation Techniques for Digamma Function

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
static CumulativeSeriesEstimator	AbramowitzStegun2007(int termCount)	Compute the Abramowitz-Stegun (2007) Cumulative Series of Digamma Estimator
static CumulativeSeriesEstimator	Asymptotic()	Compute the Asymptotic Cumulative Series of Digamma Estimator
R1ToR1Series	cumulativeSeries()	Retrieve the Underlying Cumulative Series
static CumulativeSeriesEstimator	ExponentialAsymptote()	Compute the Exponential Asymptotic Cumulative Series of Digamma Estimator
static CumulativeSeriesEstimator	ExponentialAsymptoteHalfShifted()	Compute the Exponential Asymptotic Cumulative Series of Digamma + 0.5 Estimator
static CumulativeSeriesEstimator	Gauss(int termCount)	Compute the Gauss Cumulative Series of Digamma Estimator
static CumulativeSeriesEstimator	HalfInteger()	Compute the Half-Integer Cumulative Series of Digamma Estimator
static CumulativeSeriesEstimator	Harmonic()	Compute the Harmonic Cumulative Series of Digamma Estimator
static CumulativeSeriesEstimator	MezoHoffman2017(R1ToR1 logGammaEstimator, R1ToR1 saddlePointFunction, int saddlePointCount)	Compute the Saddle-Point Cumulative Series of Digamma Estimator
static CumulativeSeriesEstimator	TaylorRiemannZeta(R1ToR1 riemannZetaEstimator, int termCount)	Compute the Taylor-Riemann Zeta Cumulative Series of Digamma Estimator

Methods inherited from class org.drip.numerical.estimation.R1ToR1Estimator

boundedEstimate, seriesEstimate, seriesEstimateNative

Methods inherited from class org.drip.function.definition.R1ToR1

antiDerivative, derivative, differential, differential, evaluate, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

AbramowitzStegun2007

public static final CumulativeSeriesEstimator AbramowitzStegun2007(int termCount)

Compute the Abramowitz-Stegun (2007) Cumulative Series of Digamma Estimator

Parameters:

termCount - Number of Terms in the Estimation

Returns:

The Abramowitz-Stegun (2007) Cumulative Series of Digamma Estimator

Harmonic

public static final CumulativeSeriesEstimator Harmonic()

Compute the Harmonic Cumulative Series of Digamma Estimator

Returns:

The Harmonic Cumulative Series of Digamma Estimator

HalfInteger

public static final CumulativeSeriesEstimator HalfInteger()

Compute the Half-Integer Cumulative Series of Digamma Estimator

Returns:

The Half-Integer Cumulative Series of Digamma Estimator

MezoHoffman2017

public static final CumulativeSeriesEstimator MezoHoffman2017(R1ToR1 logGammaEstimator,
R1ToR1 saddlePointFunction,
int saddlePointCount)

Compute the Saddle-Point Cumulative Series of Digamma Estimator

Parameters:

logGammaEstimator - The Log Gamma Estimator

saddlePointFunction - The Saddle Point Generation Function

saddlePointCount - The Saddle Point Count

Returns:

The Saddle-Point Cumulative Series of Digamma Estimator

Gauss

public static final CumulativeSeriesEstimator Gauss(int termCount)

Compute the Gauss Cumulative Series of Digamma Estimator

Parameters:

termCount - Term Count

Returns:

The Gauss Cumulative Series of Digamma Estimator

Asymptotic

public static final CumulativeSeriesEstimator Asymptotic()

Compute the Asymptotic Cumulative Series of Digamma Estimator

Returns:

The Asymptotic Cumulative Series of Digamma Estimator

ExponentialAsymptote

public static final CumulativeSeriesEstimator ExponentialAsymptote()

Compute the Exponential Asymptotic Cumulative Series of Digamma Estimator

Returns:

The Exponential Asymptotic Cumulative Series of Digamma Estimator

ExponentialAsymptoteHalfShifted

public static final CumulativeSeriesEstimator ExponentialAsymptoteHalfShifted()

Compute the Exponential Asymptotic Cumulative Series of Digamma + 0.5 Estimator

Returns:

The Exponential Asymptotic Cumulative Series of Digamma + 0.5 Estimator

TaylorRiemannZeta

public static final CumulativeSeriesEstimator TaylorRiemannZeta(R1ToR1 riemannZetaEstimator,
int termCount)

Compute the Taylor-Riemann Zeta Cumulative Series of Digamma Estimator

Parameters:

riemannZetaEstimator - The Riemann-Zeta Estimator

termCount - Term Count

Returns:

The Taylor-Riemann Zeta Cumulative Series of Digamma Estimator

cumulativeSeries

public R1ToR1Series cumulativeSeries()

Retrieve the Underlying Cumulative Series

Returns:

The Underlying Cumulative Series