(357 ) 



F„- 1 Z7;^ = _ 1 J_ [ F„_ , _ i cr^, ,,]^n[ F„_i - i C7„_i] + ^ .-26 . . (8) 

 by which we can reduce tlie evahiation of Vn — k Un to that of 



Let us now determhie the value of V^ U^. To this end we 



start from the equation (c) ; this becomes for ?i = 



1 ^^^0 1 dV, 

 2b db' '^ 2b' db 



— 2b\e 



h 



'ƒ• 



dx 



-26 _ 



2b' 



-26 



By substituting in this integral — for x we find 



OC 



ƒ• 



dx 



^I- 



62 



n-.' b 

 b 1 



hence the preceding equation becomes 

 I d'V. 1 dV. 



dz = — iU ~V\ 



u. 



4 db^ 4b db 

 By subtracting from this according to (5) 



^+^— <^+i) 



o = L'lIi_l'!I^_ V _'" 



-26 



4 db-" 4b db 



4b 



we find 



1 1 



"22 

 With the aid of equation (8) we get : 



^u.=fb-^y 



F, l\ = [b + -\e-^-^, 



1 /36^ 



V, 



1 



U, — {2b' + hP -f 6Z> + 3) 6-26 , 



F, - — U, = f^ b' + 106' + 21b' -\~ 2hb -{-I2\e- 

 in which we can easily trace the following law : 



2 " 2L n! ^d![n-l)! 5/(n-2)/ ^ 



-26 



-26 



(9) 



(10) 



Out of equation (8) and this one it is evident that Vn-^i Un-\-\ 



follows the same law; so the relation (10) is proved. 



