
/** Derivative of the Generalized Hypergeometric Function  **/
/*A: K McIsaac*/
/*S: University of Western Australia, Nedlands 6009, Australia*/
/*D: January, 1987 */
/*K: D, derivative, Ghg, Hg, Hypergeometric */
/*B:  */
/* Define the derivative of the Generalized Hypergeometric Function   */

Poc[$x,1] : $x

D[Ghg[$p,$q,#[$$a],#[$$b],$z],{$z,$n,$pt}] :: \
	Ap['Mult,Map[Poc[$1,$n],{$$a}]]/Ap['Mult,Map[Poc[$1,$n],{$$b}]] \
	Ghg[$p,$q,Ap['#,Map[$1+1,{[$$a]}]],Ap['#,Map[$1+1,{[$$b]}]],$pt]

/*F: Should include the special cases for 2F1's from A&S (p557 15.2)*/
/*E:
SMP 1.5.0   (May 14 1986)
Thu Jan  8 16:12:08 1987


#I[1]::  <XGhgPR; <XGhgD;

#I[2]::  Ghg[3,2,#[a,b,c],#[d,e],z]

	    |a,b,c |
#O[2]:*   F |     z|
	 3 2|d,e   |

#I[3]::  D[%,z]

		  |1 + a,1 + b,1 + c |
	 a b c  F |     	    z|
	       3 2|1 + d,1 + e       |
#O[3]:*  -----------------------------
		      d e

#I[4]::  <end>
*/
