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BELL SYSTEM TECHNICAL JOURNAL 



Non-Linear Devices Specified by Integrals 

 I 



— r F{iu)e'^"du 

 2x Jc 



APPENDIX 4B 



The Function iFi(a; c; x) 

 In problems concerning a sine wave plus noise the h3^ergeometric func- 



tion 



,F,(a; .; .) = 1+ -, + ^^^-^ -, + 



(4B-1) 



arises. Here we state some of its properties which are of use in the theory 

 of Part IV. Curves of iF\{a; c; z) are given for a = — 4, — 3.5 • • • , 3.5, 

 4.0 and c = - 1.5, - .5, + .5, 1, 1.5, 2, 3, 4 in the 1938 edition, page 275, 

 of "Tables of Functions", by Jahnke and Emde. A list of properties of the 

 function and other references are also given. In addition to these refer- 

 ences we mention E. T. Copson, "Functions of a Complex Variable" (Ox- 

 ford, 1935), page 260. 



If c is not a negative integer or zero 



iFi(a; c; z) = e\Fi{c — a; c; — z). 



(4B-2) 



