152 BELL SYSTEM TECHNICAL JOURNAL 



and then eliminating iFi(a + 1 ; c; s) from this relation and the one obtained 

 from row 3 of the table. There results 



iFi(a; c; z) = ,Fi{a; c - 1; z) + _ F{a + 1; c + I; z) (4B-7) 



C{^1 c) 



Setting V equal to zero and one in (4B-4) and a equal to §, c equal to 2 in 

 (4B-7) gives 



1^1 (^ ^ 5 ^) = 42"'^^ ' h (0 (4B-8) 



Starting with these relations the relations in the table enable us to find 

 an expression for iFi{n + h; m; z) where n and m are integers. A number 

 of these are given in Bennett's paper. In particular, using (4B-2), 



lF^ (-^ ; 1; -z) = e-'" [(1 + z)h (0 + zh (|)] . (4B-9) 



APPENDIX 4C 



The Power Spectrum Corresponding to ^" 

 Quite often we encounter the integral 



Gn(f) = f [rP{r)T COS iTfrdr (4C-1) 



where \P{t) is the correlation function corresponding to the power spectrum 

 w(/). From the fundamental relation between w{f) and \P{t) given by 

 (2.1-5), 



Gi(/) = ""-^ (4C-2) 



The expression for the spectrum of the product of two functions enables us 

 to write Gn{f) in terms of w{f). We shall use the following form of this 

 expression: Let Fr{f) be the spectrum of the function iprir) so that 



^r(r) = f^riDe'^^'-df, r = l,2 



J—ao 



00 



—2irifT 



dt 



