On the relation between the growth and the Taylor coefficients of entire solutions to the higher-dimensional Cauchy--Riemann system in \(\mathbb R^{n+1}\) (Q860612)
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scientific article; zbMATH DE number 5083311
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the relation between the growth and the Taylor coefficients of entire solutions to the higher-dimensional Cauchy--Riemann system in \(\mathbb R^{n+1}\) |
scientific article; zbMATH DE number 5083311 |
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On the relation between the growth and the Taylor coefficients of entire solutions to the higher-dimensional Cauchy--Riemann system in \(\mathbb R^{n+1}\) (English)
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9 January 2007
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The authors establish an interesting relation between the coefficients of the Taylor expansion of entire holomorphic functions in Clifford analysis and the growth order of the maximum modulus which is known from classical function theory. This allows to determine the growth order without knowing the maximum modulus. Examples of any finite order are given, the generalized trigonometric functions have the order 1.
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Clifford analysis
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growth orders
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entire holomorphic functions
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maximum modulus
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generalized trigonometric functions
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0.8919974
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0.8906679
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0.8885366
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