On the incomplete gamma function and the neutrix convolution

Brian Fisher; Biljana Jolevska-Tuneska; Arpad Takači

Mathematica Bohemica (2003)

  • Volume: 128, Issue: 4, page 367-377
  • ISSN: 0862-7959

Abstract

top
The incomplete Gamma function γ ( α , x ) and its associated functions γ ( α , x + ) and γ ( α , x - ) are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions x r and x - r are then found.

How to cite

top

Fisher, Brian, Jolevska-Tuneska, Biljana, and Takači, Arpad. "On the incomplete gamma function and the neutrix convolution." Mathematica Bohemica 128.4 (2003): 367-377. <http://eudml.org/doc/249218>.

@article{Fisher2003,
abstract = {The incomplete Gamma function $\gamma (\alpha ,x)$ and its associated functions $\gamma (\alpha ,x _+)$ and $\gamma (\alpha ,x _-)$ are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions $x^r$ and $x_-^r$ are then found.},
author = {Fisher, Brian, Jolevska-Tuneska, Biljana, Takači, Arpad},
journal = {Mathematica Bohemica},
keywords = {Gamma function; incomplete Gamma function; convolution; neutrix convolution; Gamma function; incomplete Gamma function; convolution; neutrix convolution},
language = {eng},
number = {4},
pages = {367-377},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the incomplete gamma function and the neutrix convolution},
url = {http://eudml.org/doc/249218},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Fisher, Brian
AU - Jolevska-Tuneska, Biljana
AU - Takači, Arpad
TI - On the incomplete gamma function and the neutrix convolution
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 4
SP - 367
EP - 377
AB - The incomplete Gamma function $\gamma (\alpha ,x)$ and its associated functions $\gamma (\alpha ,x _+)$ and $\gamma (\alpha ,x _-)$ are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions $x^r$ and $x_-^r$ are then found.
LA - eng
KW - Gamma function; incomplete Gamma function; convolution; neutrix convolution; Gamma function; incomplete Gamma function; convolution; neutrix convolution
UR - http://eudml.org/doc/249218
ER -

References

top
  1. Introduction to the neutrix calculus, J. Analyse Math. 7 (1959–60), 291–398. (1959–60) MR0124678
  2. Neutrices and the convolution of distributions, Univ. u Novom Sadu Zb. Prirod.-Mat. Fak. Ser. Mat. 17 (1987), 119–135. (1987) MR0939303
  3. On the incomplete Gamma function, submitted for publication, . 
  4. Generalized Functions, vol. I, Academic Press, 1964. (1964) MR0166596
  5. Higher Transcendental Functions, vol. I, McGraw-Hill, New York, 1953. (1953) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.