                /**  Gamma function  **/
 
/*K: Euler Gamma function; Euler integral of first kind */
 
/*A: S.Wolfram */
/*S: California Institute of Technology */
/*D: February 1982 */
 
<<XPocV
/* Recurrence relations */
 
SGamma[1,1] : Gamma[$z] -> ($z-1) Gamma[$z-1]
 
SGamma[1,2] : Gamma[$z] -> Gamma[$z+1]/$z
 
/*: CanGam[$expr,$reps]
        applies recurrence relations until the arguments of all Gamma
        functions in $expr are canonical, and vanish when the replacements
        $reps are applied. */
 
        CanGam[$expr,$reps] :: S[$expr,Gamma[$1_=Intp[Ex[S[$1,$reps]]]] --> \
                (Lcl[%z,%n]; %n:Ex[S[$1,$reps]]; %z:Ex[$1-%n]; \
                Poc[%z,%n] Gamma[%z])]
 
/*E:
SMP 1.5.0   (May 14 1986)
Mon Feb 23 11:28:05 1987


#I[1]::  <XGammaS

#I[2]::  t:Gamma[2-e/2]+Gamma[4+e]Gamma[1-e]

#O[2]:   Gamma[2 - e/2] + Gamma[1 - e] Gamma[4 + e]

#I[3]::  CanGam[t,e->0]

	 -e Gamma[-e/2] (1 - e/2)
#O[3]:   ------------------------
		    2

		    2
		 - e  Gamma[-e] Gamma[e] (1 + e) (2 + e) (3 + e)

#I[4]::  CanGam[t,e->1]

#O[4]:   Gamma[2 - e/2] + e Gamma[-1 + e] Gamma[1 - e] (-1 + e) (1 + e) (2 + e)

			  * (3 + e)

#I[5]::  <end>
*/
/*Q: XPocV, XGammaV */
