DIFFERENTIAL EQUATIONS 199 



9.132 Limiting values for x = : 



sin ( x } 

 Y (S ) _ V _V, 



JL Q Y*V/ ~~ / 



i ^2 



in(.-j) 



sin 

 7" ^v^ - 



^/ \ \^ / ~ 



V' 



9.140 Bessel's Addition Formula: 



k=o 



9.141 Multiplication formula: 



9.142 



where 



S\(k- s)\T 

 s=o 



9.143 



k=0 



DEFINITE INTEGRAL EXPRESSIONS FOR BESSEL'S FUNCTIONS 



9.150 



2 - 



/-T 



r / 2 cos (of sin </>) cos 2i; </)- 



^ ' 



9151 2 



cos (x cos (/)) sin 



