Package org.drip.specialfunction.incompletegamma

Class UpperSFixed

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.numerical.estimation.R1ToR1Estimator
org.drip.specialfunction.incompletegamma.UpperSFixed
public abstract class UpperSFixed
extends R1ToR1Estimator
UpperSFixed implements the Upper Incomplete Gamma Function using the Power Expansion Series, starting with s = 0 if Recurrence is employed. The References are:

  • Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of Definite Integrals involving Elementary Functions via Differentiation of Special Functions Applicable Algebra in Engineering, Communications, and 1 (2) 149-165
  • Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015): Tables of Integrals, Series, and Products Academic Press
  • Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over eiÏ€x x(1/x) between 1 and ∞ https://arxiv.org/pdf/0912.3844.pdf arXiV
  • National Institute of Standards and Technology (2019): Incomplete Gamma and Related Functions https://dlmf.nist.gov/8
  • Wikipedia (2019): Incomplete Gamma Function https://en.wikipedia.org/wiki/Incomplete_gamma_function
It provides the following functionality:
  • Compute the NIST (2019) Version of Upper Incomplete Gamma s = 0 Estimator
  • Compute the Weisstein Version of Upper Incomplete Gamma Estimator
  • UpperSFixed Constructor
  • Retrieve the Underlying Upper S Fixed Series
  • Evaluate the Upper Gamma (-n, z) recursively from n = 0

Module Computational Core Module
Library Function Analysis Library
Project Special Function Implementation and Analysis
Package Upper/Lower Incomplete Gamma Functions
Author:
Lakshmi Krishnamurthy

  • Method Details

    • NIST2019

      public static final UpperSFixed NIST2019​(int termCount)
      Compute the NIST (2019) Version of Upper Incomplete Gamma s = 0 Estimator
      Parameters:
      termCount - Number of Terms in the Estimation
      Returns:
      NIST (2019) Version of Upper Incomplete Gamma s = 0 Estimator

    • Weisstein

      public static final UpperSFixed Weisstein​(int s)
      Compute the Weisstein Version of Upper Incomplete Gamma Estimator
      Parameters:
      s - s
      Returns:
      Weisstein Version of Upper Incomplete Gamma Estimator

    • upperSFixedSeries

      public R1ToR1Series upperSFixedSeries()
      Retrieve the Underlying Upper S Fixed Series
      Returns:
      The Underlying Upper S Fixed Series

    • seriesEstimateNative

      public R1Estimate seriesEstimateNative​(double x)
      Description copied from class: R1ToR1Estimator
      Compute the Built-in Higher Order Series Estimates
      Overrides:
      seriesEstimateNative in class R1ToR1Estimator
      Parameters:
      x - X
      Returns:
      The Built-in Higher Order Series Estimates

    • evaluateRecursive

      public double evaluateRecursive​(int n, double z) throws java.lang.Exception
      Evaluate the Upper Gamma (-n, z) recursively from n = 0
      Parameters:
      n - n
      z - z
      Returns:
      Upper Gamma (-n, z)
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid