HEA VI SIDE'S EXPANSION THEOREM 485 



1 ^a^^" 



r(2/7T 



M, a) = ^,^,: , ^^ I'" g-^"^rfX, 



V i\X 



'a»-li(»-i)/» 



r ^ — ^ + 



Equivalent No. 4: 

 Let 



g = /)- = 



Then 



g _ ^2 



q — a p^ — a 

 Equivalent No. 5: 

 Let 



d V 



Then 



= cosh a^iH. (10) 



^ = ^ =^dt^ ' 



^— = -f^ = (l/3)€«'/'' + {2l3>)e--'''^'-^ cos (a'iHi^\ • (H) 

 — a^*^ — a \ 2/ 



q — a p^ — a 



Equivalent No. 6: 

 Let 



. = /.-■"" 



Then 



— ^ = -j^ = i cosh {a^iH) + i cos {a^'H). (12) 



g — a p — a 



Equivalent No. 7: 



Let 



d . , \i/2 



Then 



^=(^ + *)'"=(s + 0' 



_«_= _i ?!_e(..-», + "•>'* erf (VaJ) 



q — a h — a^ b — d^ b — a- 



- , ^' ., e^"'-'')^ erf (aV/j. 

 b — a- 



where b ^ a^ 



Equivalent No. 8: 

 Let 



1/2 



