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Bonding, Structure and Solid-State Chemistry$

Mark Ladd

Print publication date: 2016

Print ISBN-13: 9780198729945

Published to Oxford Scholarship Online: May 2016

DOI: 10.1093/acprof:oso/9780198729945.001.0001

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(p.401) A7 Gamma Function Γ‎‎(n)

(p.401) A7 Gamma Function Γ‎‎(n)

Bonding, Structure and Solid-State Chemistry

Mark Ladd

Oxford University Press

The gamma function [1; 2] is useful in handling integrals of the type:


where a is a constant and n is a positive number. The integrals occur in studying inter alia quantum chemistry and atomic scattering factors. The gamma function may be defined by the equation:


The following results are useful.

  1. 1. For n > 0 and integral:


  2. 2. For n > 0 and not necessarily integral:


    but if n is also integral, then:

    Γ(n+1)=n!(which follows also from 1)

(p.402) The reduction formula can also be useful:


References A7

Bibliography references:

[1] Margenau H and Murphy GM. The Mathematics of Physics and Chemistry. van Nostrand, 1943.

[2] eFunda Inc. Γ‎‎-function finder, 2015. http://www.efunda.com/math/gamma/findgamma.cfm