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2 Fasciculi Mathematici

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Growth and approximation errors of entire series having index-pair (p,q)

Khan H H, Ali R

Fasciculi Mathematici

2012

Nr 49

61--73

In this paper we Studied the polynomial coefficients and approximation errors for functions of the form f (z) = Σ∞ k=1 qk(z)[y(z)]k-1 belong to Ls (B), the class of all functions holo- morphic on Caratheodory domain B. The lower (p, q)-order and generalized lower (p, q)-type with respect to proximate order have been characterized in terms of these polynomial coefficients and approximation errors.

Approximation of entire harmonic functions in R3 in Lß - norm

Kumar D., Kasana H. S.

Fasciculi Mathematici

2004

Nr 34

55-64

A function which is harmonic in a neighbourhood of the origin in R(3) has there an expansion in spherical harmonics. For HK, he class of all harmonic functions regular in and continuous on DR , the closure of DK, we define approximation error as , is the set of all harmonic polynomials of degree at most n. In this paper we have obtained the necessary and sufficient condition on the rate of decrease of has an analytic continuation as an entire harmonic function with (p, q) - growth.