0 ea) 1 
h 
b\h > hi Aa?b? 
= Af — B wes 0 0 bie kate == 
a 9 (a?-+ 57)? 
fen | 1 F 
= 2 9 yv | 2 + u 
| 0 —1 +1 
BA 2ab 
GE Pk ek 0 Mr en ae 
a a’ +b? 
—2yv—h vp+i+h vt}h+h | 
0 —] 1! 
a+b \2h 2ab 
a= EQ —h 0 nl tyra ee 
a a’? + 5? 
—2y vtt v+h-+h 
0 oo 1 
dab 
—h ee 
(«$y 
Bap ot epe 
B he P eae 4ab 
GE) rees en fe) 
So finally we have 
6? 4ab 
azh FP (—#. —v—h, v+1, =) = (a+b) F(—A, v4+4, 2v+1, —-— ], 
| a (a+b) 
a transformation given by Gauss. 
We now substitute for the just given hypergeometrical series the 
integral 
1 
NL Oe en 
Varwtd) J” hen ‘(1 at mig 
and we find if in the integral we put z= cos? 5 
ath F( -h, -v-h, v+1 =) = mee) fete 2ab cos 7)! sin?” p d 
5 rde) Ami 4) =.) == 2a EE = / } á C . 
a)” Varetd, Eee 
In the development found for the product ./’ (az) /(bx) the above 
mentioned integral is introduced. 
Putting 
a? + Bb? — 2ab cos p = Q’, 
we obtain 
