54 



Art. 7. — K. Terazawa ; 



Uz 



■^nafx '' 



/■ a 

 c~''^ sin ]i:aJo{Ji:r)dk 



+ 



47Ta{X + fx]i. 





sin^-aJ",/^'^') 



äli 



(114) 



The integration can be carried out by expanding öin/;« into a 

 ]»ower series and making use of the formulae (42). Thus we 

 olitain 





77 



-2- 



(-Î)" 



- / 



4to(;.+/^) i^^ 27?(2w + l) \ v^- + ^- 



> (115) 



where 



VrH/ 



These series apply for the region ^r^+z^ > a. 



As in the last example, the expressions which may be applied 

 for small values of r and z can be found by using the power 

 series of the Bessel function and the formula 



./ 



Ä;"«'^* sill Art . dli = 



n ! 



{z' + a?y 



n+l 



sm 



r(n+l)tau-i-^1 



Thu^ 



Ij For 71 = we have to take P,-^(v). 



