These may be helpful: (1) http://home.iitk.ac.in/~dasgupta/MathBook/lmastertrans.pdf (2) Essentials of Mathematica: With Applications to Mathematics and Physics

By Nino Boccara

Dear Godase.

While not explicitly stated, the following link enunciates difference- and differential operators that yield generalized Fibonacci sequences and functions with extensions to the complex domain, and addresses an arsenal of open questions in mathematics, such as generalized Riemann Zeta functions, Gamma- and Polygamma functions, with wast applications to both mathematics and physics:

https://www.researchgate.net/publication/301958832_Complete_updated_On_Natural_Recursions

Furthermore - its terminating remark is as follows:

-- sincerely yours,

Gudlaugur Kristinn.

Article Complete & updated: On Natural Recursions

Dear Godase

I think it is better you ask your question by Prof. Morsaleen, from Aligarh Muslim University, his email is: [email protected]

Dear Godase,

You can consider  the book  by  Thomas Koshy,

Fibonacci and Lucas Numbers with Applications.

''This volume represents the first attempt to compile a definitive history and authoritative analysis of these famous integer sequences, complete with a wealth of exciting applications, enlightening examples, and fun exercises that offer numerous opportunities for exploration and experimentation.''