II. IV. N'. 73. THEORIE, PROPRIÉTÈS, FORMULES DE TRANST0R3I\TI0N, 



== 1e-Pll{e~<iy—(fly)f[y)Jrj-\-'^e-'-M j f{y)d,j -\-^{eP^ + e-l"}) j e~9y f (y) dy ' , 



n p-t 'p+i j 



= -(eP?+e-W) / c-<}.vf{y}dy j [e''V-y)<l^éy—p)<l]f{y)dy — I 



n fP+'^ n fP + ' 

 (eP9 -f e-/'?) 1 e-iyf{y)dy-^- c--w ƒ f {y) dy\ • • (268) 



''"■ ^'' [>«<p<'-; 



= ~ (eP9 + e-Pi) j e-iyf{y) dy —~^ j\e9y + e-9y)f(p - y) dy + \ 



a O I 



+ i / ^"'^ {-f^P - y) —fiP+y)) ^2/ + ^ ^"'''^ Hl-e-iy) f(p-\-y) dy ; j 

 •o —■ i 



^'"xSin.px f<= TT fc 

 " , , ^, ^^ ƒ f{y)Cos.xydy = -e-Pï I {eiv + e-iy}/ (y)dy , p>c; (2G9) 



= _(e-/'7 — er?) ƒ e-v>/f(y)dy , p<a- (270) 



^^e-Pl j yiy -\- e-vi)f[y)dy + ^e-2/'? i'f[y)dy = ^«-P? ƒ (c??/ + e-']!i)f{y)dy + 



a c — ; a 



-|- - e-Pi I [e—pi— ei'J — e-iy)f(y) dy , p = c; (271) 



* / 



= ^ (e-w — eP7) I e-<iyf{y] dy -|- ^ e-^ri ("/{y) dy = "^ {e-Pi - cV'i) j e-iyfiy) dy -f- 



+ - ƒ {e~^P9-\-eiP-y''] — e-(P+y)'3}fiy)dy , p = a; (272) 



a 

 7t fP~^ , TT p+e TT /"«^ 



= 7«~P' I (e1V-\-e-iy)f(y)dy-\--e-'2p<l I f (y) dy -\- - {e-Pl — ePl) I e-iyf{ydy 

 = ^(e-p?_fP?) 1 e-'Jyfiy)dy + -^ i'\Jy-p)l -\- e'P-y)i)f{y)dy -\- 



f 'a 



+ 1 (cpg — e-ï>?) j^e-iyfiy) dy-^-"^ e'^-Pi i^f{y) dy\ ■ ■ (273) 

 'p-t P-'' 



= 1 {e-P<i - ePi) j e~i!!f(y) cfy + ^ Tfew + e-7y)/(/' — y)dy + 



a "o 



+ 1 ^e-?y(/(;>-f-2/)_/(p_j/)}rfy-|-^e-5p? j\l-e-iv)/{p+y)dy. 



Paije 176. 



