Numerical calculation of incomplete gamma functions by the trapezoidal rule

1986 ◽  
Vol 50 (4) ◽  
pp. 419-428 ◽  
Author(s):  
Giampietro Allasia ◽  
Renata Besenghi
Keyword(s):  
Numerical Calculation ◽  
Trapezoidal Rule ◽  
Gamma Functions ◽  
Incomplete Gamma Functions

scholarly journals MORE SPECIAL FUNCTIONS TRAPPED

2013 ◽  
Vol 24 (02) ◽  
pp. 1350004
Author(s):  
CHARLES SCHWARTZ
Keyword(s):  
Hypergeometric Function ◽  
Bessel Functions ◽  
Special Functions ◽  
Mathematical Physics ◽  
Confluent Hypergeometric Function ◽  
Trapezoidal Rule ◽  
Integral Representations ◽  
Gamma Functions ◽  
Incomplete Gamma Functions

We extend the technique of using the trapezoidal rule for efficient evaluation of the special functions of mathematical physics given by integral representations. This technique was recently used for Bessel functions, and here we treat incomplete gamma functions and the general confluent hypergeometric function.

scholarly journals New fractional inequalities of Hermite–Hadamard type involving the incomplete gamma functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Faraidun Hamasalh ◽  
...  
Keyword(s):  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Gamma Functions ◽  
Incomplete Gamma Functions ◽  
Type Integral

AbstractA specific type of convex functions is discussed. By examining this, we investigate new Hermite–Hadamard type integral inequalities for the Riemann–Liouville fractional operators involving the generalized incomplete gamma functions. Finally, we expose some examples of special functions to support the usefulness and effectiveness of our results.

scholarly journals Incomplete gamma functions for large values of their variables

2005 ◽  
Vol 34 (3) ◽  
pp. 467-485 ◽  
Author(s):  
Chelo Ferreira ◽  
José L. López ◽  
Ester Pérez Sinusía
Keyword(s):  
Gamma Functions ◽  
Incomplete Gamma Functions

The incomplete gamma functions

2016 ◽  
Vol 100 (548) ◽  
pp. 298-306 ◽  
Author(s):  
G. J. O. Jameson
Keyword(s):  
Gamma Function ◽  
Incomplete Gamma Function ◽  
Gamma Functions ◽  
Incomplete Gamma Functions ◽  
Definition Of ◽  
Image Position ◽  
Selection Of

Recall the integral definition of the gamma function: for a > 0. By splitting this integral at a point x ⩾ 0, we obtain the two incomplete gamma functions:(1)(2)Γ(a, x)is sometimes called the complementary incomplete gamma function. These functions were first investigated by Prym in 1877, and Γ(a, x) has also been called Prym's function. Not many books give these functions much space. Massive compilations of results about them can be seen stated without proof in [1, chapter 9] and [2, chapter 8]. Here we offer a small selection of these results, with proofs and some discussion of context. We hope to convince some readers that the functions are interesting enough to merit attention in their own right.

scholarly journals On a connection between the generalized incomplete gamma functions and their extensions

1997 ◽  
Vol 38 (4) ◽  
pp. 581-589 ◽  
Author(s):  
M. Aslam Chaudhry ◽  
S.M. Zubair
Keyword(s):  
Gamma Functions ◽  
Incomplete Gamma Functions

AbstractIn this paper we have proved that the generalized incomplete gamma functions and their extensions are mutually related through integral and differential representations.

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