On symbolic calculus of two variables
N. K. Chakravarty · Acta Mathematica · 1955
in Calcutta 1.The notation ~, (p, q) 0, R(q)>0, o oThe object of the present paper is to derive a theorem in the symbolic calculUs of two variables, starting from a chain of relations in one variable, and to show some applications of the theorem., Theorem..If /(p)~x'-lh(x)and ~rthen y'-~a (~ y~) > v "-~/(f q), valid when p > 0, R (X) > -1, R (~) > -1.Then Proof.Let J~(x) represent Wright's generali~d Be~el function [1] defined by 0" (-a:)' p>O, R(2)>-1.J~(x)= 9 --'9 r! F (i + ~.+~ r)' (.Ig.a+~ry'+" ~ay, j~(~a~y)_ ,-o ~: rIFll+X+pr) 1 ~F(,+r+l)( ~__~)" -7i -~(,+1~-~.q= F (v + 1)-(1 + _,,q),+ ~,/7 R(v)> -1.(2.1)