390 Mr Murphy on the Inverse MetJwd of 



oc -5^ the internal tension oc/3"; the proposed question now be- 

 comes 



To find {A) such a function of t that the value of 



f, \* + p + iffi. a-**)}* ' may be m -w" or m -^> 



according as a is less or greater than /3. 



The formula which represents the latter discontinuous function 

 (by Section II, Art. 20.) is a series of which the general term is 



1.3.5...(2*-1) x.(x-l).(x-2)...(x-u + l) , 2^'.(q/3) r 



2. 4. 6.. .2x •(arfl).(*+2).(»+8)...(#+»+l) ,v '" (a+/3) 8 ' +1 ' 



and the general term of the integral when we expand the deno- 

 minator is as before 



1.3.5...(2s-l) 2'MqffV 

 * 2.4.6...(2«) '(a + /3)"* + " 



) '(« + /3) 2 



and if ^4 receive a value such as to make the general terms 

 of both series identical, the series will also be themselves iden- 

 tical. 



Equating we get 



, , . x.(x-l).{x-2)...(x-n + l) 



f>A.t<=m.(2n + l). (x + l)(x + 2Ux + 3)M + n+1) , 



from which we may find A, by the method given in Art. 8, 

 Section V. (Vid. Ex. 4.); its value is 



n n + 1 n.(n— 1) (»+l).(» + 2) ., 

 A=m(2n + l).{-iy.\l- j.—.t+ \ _ 2 ' ■ 5^ *.*'-&<!. 



