q-Difference Recurrence Relations of Aleph Function with Generalization to nth Derivative

Sharma and Jain studied the basic analogue of Meijer’s G-function by using the methods of q -calculus and constructed the q -difference operators and their lie algebra. In this article, we employ the same technique for basic anlogue of the Aleph function defined by Dutta et al. and thus on account o...

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Bibliographic Details
Published in:International journal of applied and computational mathematics 2024-04, Vol.10 (2), Article 85
Main Authors: Bhat, Mohammad Younus, Maqbool, Humaira, Bhat, Altaf A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus
Computational Science and Engineering
Finite differences
Lie groups
Mathematical analysis
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Operators (mathematics)
Original Paper
Theoretical
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Summary:Sharma and Jain studied the basic analogue of Meijer’s G-function by using the methods of q -calculus and constructed the q -difference operators and their lie algebra. In this article, we employ the same technique for basic anlogue of the Aleph function defined by Dutta et al. and thus on account of general nature of q-analogue of Aleph function,the q -difference recurrence relations of the Aleph function are obtained and an enumerous number of new and known results are special cases of our main results. Also the recurrence relation of I-function and Fox-H function are deduced as special cases by suitable substitutions. Furthermore the generalisation to nth partial derivatives and the required relations are also discussed which are quite general in nature and capable of producing a number of new and known results.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-024-01724-6