home *** CD-ROM | disk | FTP | other *** search
/ Chip 2002 June / Chip_2002-06_cd1.bin / zkuste / derive / download / Setup.exe / %MAINDIR% / Math / Hypergeo.mth < prev    next >
Encoding:
Text File  |  2002-05-15  |  1.0 KB  |  26 lines
  1. "File HYPERGEO.MTH, copyright (c) 1990-2000 by Texas Instruments Incorporated"
  2.  
  3. "HYPERGEOMETRIC_SERIES([a1,...,ap],[b1,...,bq],z,m) computes m+1 terms"
  4. "of the generalized hypergeometric series pFq(a1,...,ap;b1,...,bq;z)."
  5.  
  6. HYPERGEOMETRIC_SERIES(plist,qlist,z,m):=SUM(PRODUCT(PERM(k_+plist SUB j_-1,k_)~
  7. ,j_,1,DIMENSION(plist))*z^k_/(PRODUCT(PERM(k_+qlist SUB j_-1,k_),j_,1,DIMENSIO~
  8. N(qlist))*k_!),k_,0,m)
  9.  
  10. KUMMER_AUX(a,b,z):=(1/2)^a/a+INT(t^(a-1)*(#e^(z*t)*(1-t)^(b-a-1)-1),t,0,1/2)
  11.  
  12. KUMMER(a,b,z):=GAMMA(b)/(GAMMA(b-a)*GAMMA(a))*(KUMMER_AUX(a,b,z)+#e^z*KUMMER_A~
  13. UX(b-a,b,-z))
  14.  
  15. KUMMER_SERIES(a,b,z,m):=HYPERGEOMETRIC_SERIES([a],[b],z,m)
  16.  
  17. GAUSS_AUX(a,b,c,z):=(1/2)^b/b+INT(t^(b-1)*((1-t)^(c-b-1)*(1-t*z)^(-a)-1),t,0,1~
  18. /2)
  19.  
  20. GAUSS(a,b,c,z):=IF(z=1,GAMMA(c)*GAMMA(c-a-b)/(GAMMA(c-a)*GAMMA(c-b)),GAMMA(c)/~
  21. (GAMMA(b)*GAMMA(c-b))*(GAUSS_AUX(a,b,c,z)+(1-z)^(-a)*GAUSS_AUX(a,c-b,c,z/(z-1)~
  22. )),GAMMA(c)/(GAMMA(b)*GAMMA(c-b))*(GAUSS_AUX(a,b,c,z)+(1-z)^(-a)*GAUSS_AUX(a,c~
  23. -b,c,z/(z-1))))
  24.  
  25. GAUSS_SERIES(a,b,c,z,m):=HYPERGEOMETRIC_SERIES([a,b],[c],z,m)
  26.