199 



This ^ve substitute: 



H,n{^) = (-1)" . '22" |>/^/4.^•^)- ^"A/. -ik^) - ^r— e^"' Ce-J^(2,v\/a) 



2\/jr J 







" n! 



We further introduce: 



00 3 





 and 



00 ao 



^■^^ r r 







We find then : 



o * 00 







or after some reduction 



(-1)"- ' ^ H,r. i^) + n! r/.„ (.t-^) z= 1 



e^ r /' - ^ i ) I 



= -— - I e-'-J^ (2.r !/''«) ^i« X^-'t ^ Ua^ty — tf' dt \ 

 ; 



F^or .1' = 0, tlie following identities arise from the formulae (6) 



and (22): 



and 



or 



22'- = 2 ^^ — ■ — -- or 2-^« = :E V^ . . (-7) 



lc=^ kr{n-k)!' i2n)f jc=or2n\ ^ ^ 



^Ml-o.. „,)1 j 1 1.3 5 .. (2^-3) 



2 k=2k! 2k 



1 " 1 1.3.5 ...{2k—o) 



^T7^ • • • (28) 



nr 2 /,— o A;/ 2^ 



22» 



(2n)J 



14* 



