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Shah, S. M.
- Summation of a Certain Series
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Authors
Affiliations
1 Department of Mathematics, S. V. Vidyapeeth, Vallabh Vidyanagar, Yia. Anand (W. Rly.), IN
2 Department of Mathematics, S. V. Vidyapeeth, Vallabh Vidyanagar, Yia. Anand (W. Rly.), IN
1 Department of Mathematics, S. V. Vidyapeeth, Vallabh Vidyanagar, Yia. Anand (W. Rly.), IN
2 Department of Mathematics, S. V. Vidyapeeth, Vallabh Vidyanagar, Yia. Anand (W. Rly.), IN
Source
The Journal of the Indian Mathematical Society, Vol 29, No 4 (1965), Pagination: 187-195Abstract
Summation of a Certain Series.
- Exceptional Values of Entire and Meromorphic Functions, II
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Authors
Affiliations
1 Muslim University, Aligarh, IN
1 Muslim University, Aligarh, IN
Source
The Journal of the Indian Mathematical Society, Vol 20, No 1-3 (1956), Pagination: 315-327Abstract
This paper is a continuation of my paper [8] and we follow the same notation.- On-The Maximum Modulus and the Coefficients of an Entire Series
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Authors
S. M. Shah
1,
M. Ishaq
2
Affiliations
1 Muslim University, Aligarh, IN
2 Luoknow University, IN
1 Muslim University, Aligarh, IN
2 Luoknow University, IN
Source
The Journal of the Indian Mathematical Society, Vol 16 (1952), Pagination: 177-182Abstract
Let f(z) =Σ∞anZn be an entire function, μ(r) the maximum term of the series for \z\ = r and v(r) its rank. A number of results connecting M(r), μ(r), v(r) and an are known [4, pp. 28-46, 93-106 ; 2, pp. 3-11 ; 3 ; 5] but some of them are true only for functions of finite order.- A Note on the Lower Order of Integral Functions
Abstract Views :180 |
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Authors
Affiliations
1 Aligarh, IN
1 Aligarh, IN
Source
The Journal of the Indian Mathematical Society, Vol 9 (1945), Pagination: 50-54Abstract
If f(z) = Σanzn is an integral function of lower order λ (0 ≤ λ ≤ ∞) such that |an/an + 1| is a non-decreasing function of n for n ≥ n0.- The Maximum Term of an Entire Series (II)
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Authors
Affiliations
1 Aligarh, IN
1 Aligarh, IN
Source
The Journal of the Indian Mathematical Society, Vol 9 (1945), Pagination: 54-55Abstract
Let μ(r) be the maximum term for |z| = r of the entire series f(z) = Σ anZn and v(r) its rank.- The Lower Order of the Zeros of an Integral Function
Abstract Views :167 |
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Authors
Affiliations
1 Aligarh, IN
1 Aligarh, IN
Source
The Journal of the Indian Mathematical Society, Vol 6 (1942), Pagination: 63-68Abstract
Let f(z) be an integral function of finite order ρ. We write
f(z)=ZkeQ(z)P(Z),
where Q(z) is a polynomial of degree q and P(Z) a canonical product of order ρ1.
- A Theorem on Integral Functions of Integral Order (II)
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Authors
Affiliations
1 Aligarh, IN
1 Aligarh, IN
Source
The Journal of the Indian Mathematical Society, Vol 5 (1941), Pagination: 179-188Abstract
Let F(z) be an integral function of finite order p. We write F(z) = ZkeQ(z)f(z), where Q(z) is a polynomial of degree q≤p, k a positive integer or zero.- Note on a Theorem of Polya
Abstract Views :191 |
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Authors
Affiliations
1 Aligarh, IN
1 Aligarh, IN
Source
The Journal of the Indian Mathematical Society, Vol 5 (1941), Pagination: 189-191Abstract
Let f(z) be an integral function of order p. G. Polya proved that
lim n(r)/log M(r) ≤p (I)
where M(r) and n(r) have their usual meanings.
- An Inequality for the Arithmetical Function g(x)
Abstract Views :185 |
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Authors
Affiliations
1 Muslim University, Aligarh, IN
1 Muslim University, Aligarh, IN
Source
The Journal of the Indian Mathematical Society, Vol 3 (1939), Pagination: 316-318Abstract
Let n = a1 + a2 + .......... + ap, and f(n) the maximum of the least common multiple of a1, a2, .. ., ap for all such positive a's. Landau has proved that if log f(x)=g(x), then
lim g(x)/(x logx)1/2 = 1. (1)
Let p denote a prime number.