833 



the arithuietieal symbol )• For the rest the}' show some similarity 



with formulae in the theory of the »>-fiinctions, and point to a 



certain connection between the functions Ö | v, — j and i) { r. 



So it may be observed, that, from the equation 



^3 0' - P-4 0' - —-^-^ = 1 f 4 ^ — ^ cos 2jr 7nv 



in the case a^=4iW-\-l, ensues 



/A i 



and the equation (V) proves that the expression 



'A i 



.-/.("7)»<%)r^'^ '■ ' 



^^ ^3 ( 0, - I ^, ( 0, - I i ' fl^—^^-^ (a .= 4i6- + 1) 



•e-f) 



^J - 



remains unchanged, if ;i is replaced by y. 

 In a similar way we conclude from 



=1 jt cot V :i: 4- 4: JT S — s/» 2jt mt 



I 1 o .,, 



v', y, — 



for the case a = 4:w — 1 to 





We can prove now, that 



:S {-]cot — = 2[/af{l) 



h=i v«y « 



consequently it ensues from the equation (VI). that the expression 



/A i 



1 /'=^-i /A\ ^' \a' 3 , 

 ^ [ _ ) ^^ 'l^ (a = 4it' — 1) 



holds its value, if 3 is changed into y. 



55* 



