On the Laguerre polynomial approximation errors and lower type of entire functions of irregular growth
It has been noted that lower type of an entire function completely ignores the value of lower order. The question arises for entire functions of irregular growth that what happens when we replace order by an arbitrary nonzero finite number. Here in this article our aim is to solve this problem by de...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-02-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2024-0096 |
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| Summary: | It has been noted that lower type of an entire function completely ignores the value of lower order. The question arises for entire functions of irregular growth that what happens when we replace order by an arbitrary nonzero finite number. Here in this article our aim is to solve this problem by defining new lower (p,q)\left(p,q)-type by using a (p,q)\left(p,q)-scale, (p≥q≥1)\left(p\ge q\ge 1) for an entire function. Moreover, a relationship has been established between lower (p,q)\left(p,q)-type of entire function solutions of linear homogeneous partial differential equation of second order with coefficients occurring in series expansion and Laguerre polynomial approximation errors in sup norm. |
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| ISSN: | 2391-4661 |