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Astronomical Applications Department, U.S. Naval Observatory - Sensitivity Integral (Page 1)

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Astronomical Applications Department, U.S. Naval Observatory - Sensitivity Integral
Evaluation of a Photon Sensitivity Integral
for the FAME Instrument
Marc A. Murison
Astronomical Applications Department
U.S. Naval Observatory, Washington, DC
murison@riemann.usno.navy.mil
http://aa.usno.navy.mil/murison/
17 March, 1997
Contents
Note: This document is actually a Maple session. Normal text is shown in Times Roman black.
Maple input is in
Courier red
and, for most, can (perhaps should) be ignored. Comments
embedded in Maple input begin with the pound symbol, #. Maple output is shown in
Times
Roman blue
for math expressions and
Courier blue
for text (informational messages). Maple
input commands are normally terminated with a semicolon; when an input command terminates
with a full colon, output to the screen is suppressed. This is a handy mechanism for suppressing
unwanted output, and I use it frequently. Hyperlinks allow you to jump around in the document;
they appear as
underlined blue
. Here is a Table of Contents for this Memo:
Introduction
1. Definite Integral
2. Indefinite Integral
3. Check of the Indefinite Integral
4. Definite Integration by Parts
5. Comparison between Definite and Indefinite Integrations
6. Singularity Surfaces in Geometry Factor Parameter Space
6.1. Series Approximations of the Integral
6.2. Graphical Representation of the Singular Surfaces
6.3. Special Case: r = s = 0
Appendix: Integration Result Expressions
Introduction
Page 1

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