Package org.drip.specialfunction.incompletegamma

Class LowerSFixedSeriesTerm

java.lang.Object
org.drip.specialfunction.incompletegamma.LowerSFixedSeriesTerm
public class LowerSFixedSeriesTerm
extends java.lang.Object
LowerSFixedSeriesTerm implements a Single Term in the Lower Incomplete Gamma Expansion Series for a Fixed s. 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:
  • Construct the Weierstrass Limit Version of the Lower S Fixed Term
  • Construct the NIST (2019) Limit Version of the Lower S Fixed Term

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

  • Constructor Summary

    Constructors
    Constructor Description
    LowerSFixedSeriesTerm()  

  • Method Summary

    Modifier and Type Method Description
    static R1ToR1SeriesTerm NIST2019​(double s, double logGammaS)
    Construct the NIST (2019) Limit Version of the Lower S Fixed Term
    static R1ToR1SeriesTerm WeierstrassLimit​(double s)
    Construct the Weierstrass Limit Version of the Lower S Fixed Term

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • LowerSFixedSeriesTerm

      public LowerSFixedSeriesTerm()

  • Method Details

    • WeierstrassLimit

      public static final R1ToR1SeriesTerm WeierstrassLimit​(double s)
      Construct the Weierstrass Limit Version of the Lower S Fixed Term
      Parameters:
      s - s
      Returns:
      The Weierstrass Limit Version of the Lower S Fixed Term

    • NIST2019

      public static final R1ToR1SeriesTerm NIST2019​(double s, double logGammaS)
      Construct the NIST (2019) Limit Version of the Lower S Fixed Term
      Parameters:
      s - s
      logGammaS - Log (Gamma (s))
      Returns:
      The NIST (2019) Limit Version of the Lower S Fixed Term