The hubbell rectangular source integral and its generalizations
A survey of the evaluation, series expansions, properties and approximation of the Hubbell rectangular source integral ƒ(a,b)= ∫ 0 b arctan a 1+x 2 dx 1+x 2 is presented. We review different generalizations of this integral ( H, G and S-integral) and examine some of their important properties, inclu...
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| Published in | Radiation physics and chemistry (Oxford, England : 1993) Vol. 41; no. 4; pp. 775 - 781 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.04.1993
|
| Online Access | Get full text |
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| Summary: | A survey of the evaluation, series expansions, properties and approximation of the Hubbell rectangular source integral
ƒ(a,b)=
∫
0
b
arctan
a
1+x
2
dx
1+x
2
is presented. We review different generalizations of this integral (
H,
G and
S-integral) and examine some of their important properties, including algorithms for their approximations. The quantity
P
l(
a, b), which describes the response of an omni-directional radiation detector as a prescribed height directly over a plane anisotropic rectangular source is expressed in terms of Appell's function
F
2. Alternative expansion coefficients
q
n
(
a, b) given by Hubbell are also represented in terms of
F
2. |
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| ISSN: | 0969-806X 1879-0895 |
| DOI: | 10.1016/0969-806X(93)90325-O |