26 



Art. 7. — K. Terazawa : 



sin-ö 



J,{kr]J,{Tia) = / J^[IB)—^ 



71 ' M 



cW 



(61) 



which follow from Neumann's addition theorem for the Bessel 

 function. Making use of these formulae and on referring to the 

 formulas (42), we obtain 



fe-"J,{j£r)J^il.a]dk = ^/ 



1 /•'^ cos<^ 



fe"'Jç,{kr)J,{ka)dk = -^ f 



cW, 



a — rcosd iß_ z /"^ a—rcosd ^a 



B' 



/ '^ ' '^ ^ I r: J B- ^ J Bl 



siii- 



J'e-'^Joih-y.ika)-^' = -^ / " V-^' + ^' (a - ?■ cos d)dd 



_ ^ f~ a—rcoaO 



71 J 



dd, 



B' 



dd 



(62) 



To find these integrals, put 



so that 



2 \i r. a'+r' + z- 



P = 

 ar 



bar 



_ 2/9 _ a- + 7-- + z~ 

 « 'à ara 



_ 1— /5 _ _ a."' + r'' + 2'' — 6ftr 



« &arf/- 



_ _ 1+/5 _ _ a?-^ r-\-z"- + ^'>ar 



()ara 



m) 



^1 + 62 + 63 = 0, 

 and change the integration variable from 6 to .5 by putting 



cos, 6 = as + ß, 



then we have 



