Connections within the group of the Fibonacci and Lucas numbers and with other function groups

Representations through more general functions

The Fibonacci and Lucas numbers and have the following representations through more general functions including some hypergeometric functions and Meijer G functions:

Representations of Fibonacci and Lucas numbers through each other and through elementary functions

The Fibonacci and Lucas numbers and can be represented through each other by the following formulas:

The Fibonacci and Lucas numbers and have the following representations through elementary functions: