K-Humbert confluent hypergeometric functions \(\Phi_{1,k}\), \(\Phi_{2,k}\), and \(\Phi_{3,k}\)
Authors
M. Arshad
- Department of Mathematics and Statistics, University of Agriculture, Faisalabad 38000, Pakistan.
M. Usman
- Department of Mathematics and Statistics, University of Agriculture, Faisalabad 38000, Pakistan.
M. Z. Iqbal
- Department of Mathematics and Statistics, University of Agriculture, Faisalabad 38000, Pakistan.
A. Ali
- Department of Mathematics, Government Graduate College of Science, Faisalabad, Pakistan.
Abstract
The main aim of this work is to introduce the k-Humbert confluent hypergeometric functions \(\Phi_{1,k}\), \(\Phi_{2,k}\), \(\Phi_{3,k}\) and developed some formulae by using the idea of k-calculus. k-Humbert confluent hypergeometric functions are an extension of the classical confluent hypergeometric functions, incorporating an additional parameter, k, which enriches their analytical properties and applicability in diverse mathematical contexts. We introduce new results by applying $q$-derivative operator on k-Humbert confluent hypergeometric functions \(\Phi_{1,k}\), \(\Phi_{2,k}\), and \(\Phi_{3,k}\). Contiguous function relations of various types, (q, k)-recurrence relations, and $q$-derivatives formulae are constructed.
Share and Cite
ISRP Style
M. Arshad, M. Usman, M. Z. Iqbal, A. Ali, K-Humbert confluent hypergeometric functions \(\Phi_{1,k}\), \(\Phi_{2,k}\), and \(\Phi_{3,k}\), Journal of Mathematics and Computer Science, 35 (2024), no. 3, 348--361
AMA Style
Arshad M., Usman M., Iqbal M. Z., Ali A., K-Humbert confluent hypergeometric functions \(\Phi_{1,k}\), \(\Phi_{2,k}\), and \(\Phi_{3,k}\). J Math Comput SCI-JM. (2024); 35(3):348--361
Chicago/Turabian Style
Arshad, M., Usman, M., Iqbal, M. Z., Ali, A.. "K-Humbert confluent hypergeometric functions \(\Phi_{1,k}\), \(\Phi_{2,k}\), and \(\Phi_{3,k}\)." Journal of Mathematics and Computer Science, 35, no. 3 (2024): 348--361
Keywords
- Humbert confluent hypergeometric functions
- $q$-derivative
- (q, k)-recurrence relations and contiguous function
MSC
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