On the generalized type and approximation of an entire harmonic function in R3 having index pair (p,q)

Let H/?, 0< R <oo,bethe class of all harmonic functions H R3 that are regular in the open ball DR of radius R centered at the origin and continuous on the closure DR of DR. For He // K, set En (H,R) = inf < max \H(xi>x2>x-i) - g(xi,x2>x3) \ >, geI7» {(xux2,x,)eDR ' J where ITK consists of all harmonic polynomials of degree at most n. In the present paper, we have introduced the concept of (p,q)~ type of an entire harmoni'C function H with respect to the proximate order with index pair (p,q) and obtained its coefficient characterization in term of the approximation errors En (H, R).