RESPONSE OF RECTIFIER TO SIGNAL AND NOISE 109 



aPo 



+ 2 





(eri?^^)de 



do \ V2Wn/ 



^ a_ -yWn ^-W,/2W„ r" ^-W, cos */2If„ j^ 



2ir lir Jo 



= " i/r-" '"■'''"'" (wv./2w„) 



+ 2j [7o(T7./2TF„) + h{Wj2Wn)]\ (10) 



In the above we have made use of the relations 



V 



erf s = ^ f e"'' Jz (51) 



TT Jo 



r " ^-^cos* ^^g ^^^^ ^^ ^ (-)'"27r7„(2) (53) 



Jo 



APPENDIX II 



RELATIONS BETWEEN HYPERGEOMETRIC AND BESSEL 



FUNCTIONS 



The modulation coefficients appearing in the linear rectification of noise 

 are expressible in compact form in terms of the hypergeometric function: 



(54) 



^ r(£) y V{a + m) ^ . 

 V{a) £^oV{c-\-m)m\^ ^ 



The iFi function is a limiting case of the more familiar Gaussian hypergeo- 

 metric function ^Fi (o, h; c; z), viz. 



iFi(a; c, z) = Limit 2Fi(a, b; c; z/b) (55) 



6=00 



In certain special cases this function may be expressed in terms of ex- 

 ponential and Bessel functions. For example, by a formula given by 



