On Entire Functions of Fast Growth

Bajpai, S. K.; Kapoor, G. P.; Juneja, O. P.

doi:10.2307/1997084

Transactions of the American Mathematical Society

1975

DOI: 10.2307/1997084

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On Entire Functions of Fast Growth

S. K. Bajpai¹,

G. P. Kapoor²,

O. P. Juneja³

Abstract: ABSTRACT. Let () A) = V"z " n=0 be a transcendental entire function. Set Ai(r) = max \fiz)\, m(r) = max {la \r "} \z\=r n>0and N(r) = max {XJm(r) = \a"\r "}. For the case q = 2, these notions are due to Whittakar and Shah respectively.

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“…Theorem 3 generalizes a result of Bajpai [1] which was derived for (p^ q) = (p, 1) and λ 1ΰ = k. For (p, q) = (2, 1), the corollary was obtained by Gray and Shah [3] by a different technique. Therefore, -flog | a k Γ 1 ^ log V ( -1) (l-Λ Α which gives L Ξ> L* for every entire function having index-pair (p, g), p Ξ> 2.…”

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confidence: 76%

On the (p, q)-order and lower (p, q)-order of an entire function.

1976

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Goefficient equivalents of ρ and T are known (see e. g. [2], pp. 9-12).If f(z) is of infinite or zero order, the definition of type is not feasible and so growth of such functions cannot be precisely measured by confining to the above concepts. For functions of infinite order, Sato [8] introduced the concept of 'index' of an entire function. Thus, if (1.3) Journal f r Mathematik. Band 282Brought to you by | University of Iowa Libraries Authenticated Download Date | 6/13/15 9:44 PM Q(Pn,q) = oo (n < p), ρ(ρ^η) = 0 (n < q) and ρ (p + n, q + n) = l for n = 1,2, ____ If (x, y) is any pair of integers satisfying y = χ + q -p and χ < p, then ) = 0 if 0 < ρ(ρ, q) < l and Q(X, y) = oo if l < ρ(ρ, q) < σο.

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supporting

confidence: 76%

On the (p, q)-order and lower (p, q)-order of an entire function.

1976

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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show abstract

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On Entire Functions of Fast Growth

Abstract: ABSTRACT. Let () A) = V"z " n=0 be a transcendental entire function. Set Ai(r) = max \fiz)\, m(r) = max {la \r "} \z\=r n>0and N(r) = max {XJm(r) = \a"\r "}. For the case q = 2, these notions are due to Whittakar and Shah respectively.

Cited by 1 publication

References 4 publications

On the (p, q)-order and lower (p, q)-order of an entire function.

On the (p, q)-order and lower (p, q)-order of an entire function.

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On Entire Functions of Fast Growth

Abstract: ABSTRACT. Let (*) A*) = V"z " n=0 be a transcendental entire function. Set Ai(r) = max \fiz)\, m(r) = max {la \r "} \z\=r n>0and N(r) = max {XJm(r) = \a"\r "}. For the case q = 2, these notions are due to Whittakar and Shah respectively.

Cited by 1 publication

References 4 publications

On the (p, q)-order and lower (p, q)-order of an entire function.

On the (p, q)-order and lower (p, q)-order of an entire function.

Contact Info

Product

Resources

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Abstract: ABSTRACT. Let () A) = V"z " n=0 be a transcendental entire function. Set Ai(r) = max \fiz)\, m(r) = max {la \r "} \z\=r n>0and N(r) = max {XJm(r) = \a"\r "}. For the case q = 2, these notions are due to Whittakar and Shah respectively.