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Internet Message Format  |  1992-11-17  |  1.5 KB
  1. Path: sparky!uunet!charon.amdahl.com!pacbell.com!decwrl!sun-barr!cs.utexas.edu!wupost!usc!hacgate!rigel!abirenbo
  2. From: abirenbo@rigel.cel.scg.hac.com (Aaron Birenboim)
  3. Newsgroups: comp.compression
  4. Subject: Re: Math Question
  5. Message-ID: <24017@hacgate.SCG.HAC.COM>
  6. Date: 16 Nov 92 15:41:22 GMT
  7. References: <24005@hacgate.SCG.HAC.COM>
  8. Sender: news@hacgate.SCG.HAC.COM
  9. Organization: Hughes Aircraft Colorado Engineering Labs
  10. Lines: 39
  11.  
  12. In article <24005@hacgate.SCG.HAC.COM> abirenbo@rigel.cel.scg.hac.com (Aaron Birenboim) writes:
  13. >
  14. >While working on an optimization problem related to compression
  15. >I bumped into the following nasty little problem :
  16. >
  17. >   evaluate:
  18. >
  19. >                {           [(i+1)q                                      }
  20. >             d  {           [                                            }
  21. >            --- {  Integral [      (x - (i + 0.5) q)^2 * exp(-c * x) dx  }
  22. >             dq {           [                                            }
  23. >                {           [i*q                                         }
  24. >
  25.  
  26. the answer i was seeking was "Leibnitz rule".  its quite useful.
  27. Patrich smith was kind enough to send me the definition:
  28.  
  29.       / b(y)
  30. d    |
  31. --   |        f(x,y) dx   =
  32. dy   |
  33.     /  a(y)
  34.       
  35.       
  36.       
  37.     / b(y)
  38.     |        d
  39.     |        -- f(x,y) dx   +  b'(y)f(b(y),y)  -  a'(y)f(a(y),y)
  40.     |        dy
  41.     /  a(y)
  42.                   
  43. thanks to all those who replied!
  44.  
  45.  
  46. --
  47. Aaron Birenboim         |
  48. birenb@hac2arpa.hac.com |
  49.                         |
  50. H (303) 871-8271        |
  51.