Sum and Product Theorems relating to Generalized Relative Order (α, β) and Generalized Relative Type (α, β) of Entire Functions

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2021, v.28 no.2, pp.155-185

https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.2.155

Biswas, Tanmay
Biswas, Chinmay (Department of Mathematics, Nabadwip Vidyasagar College)
Saha, Biswajit (Department of Mathematics, Government General Degree College Muragachha)

Biswas, Tanmay, Biswas, Chinmay, & Saha, Biswajit. (2021). SUM AND PRODUCT THEOREMS RELATING TO GENERALIZED RELATIVE ORDER (𝛼, 𝛽) AND GENERALIZED RELATIVE TYPE (𝛼, 𝛽) OF ENTIRE FUNCTIONS. 한국수학교육학회지시리즈B:순수및응용수학, 28(2), 155-185, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.2.155

복사

Abstract

Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of generalized relative order (𝛼, 𝛽), generalized relative type (𝛼, 𝛽) and generalized relative weak type (𝛼, 𝛽) of entire functions with respect to another entire function where 𝛼, 𝛽 are continuous non-negative functions on (-∞, +∞).

keywords: entire function, growth, composition, generalized relative order (<tex> ${\alpha}$</tex>, <tex> ${\beta}$</tex>), generalized relative type (<tex> ${\alpha}$</tex>, <tex> ${\beta}$</tex>), generalized relative weak type (<tex> ${\alpha}$</tex>, <tex> ${\beta}$</tex>)

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Vol.28 No.2

SUM AND PRODUCT THEOREMS RELATING TO GENERALIZED RELATIVE ORDER (&#x1D6FC;, &#x1D6FD;) AND GENERALIZED RELATIVE TYPE (&#x1D6FC;, &#x1D6FD;) OF ENTIRE FUNCTIONS

Sum and Product Theorems relating to Generalized Relative Order (α, β) and Generalized Relative Type (α, β) of Entire Functions

Abstract

한국수학교육학회지시리즈B:순수및응용수학

SUM AND PRODUCT THEOREMS RELATING TO GENERALIZED RELATIVE ORDER (𝛼, 𝛽) AND GENERALIZED RELATIVE TYPE (𝛼, 𝛽) OF ENTIRE FUNCTIONS