Confluent Hypergeometric Function, 137 



</ = * r 



§ 4. Tables and Graphs of M(a, 7, a?). 



The following tables or" M(«, 7, a?) were calculated, for 

 small values of x, from the series in ascending powers of 

 this argument, and for large values, from the asymptotic 

 -expansions. When a and 7 are positive integers, two or 

 three values of M, for a particular value of #, are required 

 to give the other results by means of suitable recurrence 

 formulas. The last two formulas of (12) were employed to 

 find further values of M along vertical columns and hori- 

 zontal rows; the first four, to "turn the corners" and fill 

 in the results in the rectangle of values thus obtained. 

 When a is a negative integer, the M function is a poly- 

 nomial which is easily evaluated. A similar procedure 

 was adopted in the case of a equal to half an odd positive 

 or negative integer, only two preliminary calculations of M 

 being required to give the remaining 47 for each value of 

 the argument x. 



Four significant figures are given in the tables. The 

 numbers, however, must be multiplied by the power of 

 ■ten indicated by the figure after the comma. Thus, 



M(4, 1, 4) =2603; M(3, 2, 10) = 132200 ; 

 and M(-i, 4,10) =-3-419. 



