We have investigated new Pauli Fibonacci and Lucas quaternions by taking the components of these as Gaussian numbers, respectively. calculated some basic identities for quaternions. Later, generating functions Binet formulas are obtained Furthermore, Honsberger’s identity, Catalan’s Cassini’s been given

A quick glance through the Mathematics section of the 2004 Stanford University Bulletin reveals five courses devoted to complex analysis, but no courses even mentioning quaternions. How is it that complex analysis, a subject that has suffered through hundreds of years of skepticism and distrust, came to be so widely accepted today, while quaternionic analysis, a modern subject immediately accep...

In this paper Fibonacci sequences of quaternions are introduced, generalizing Fibonacci sequences over commutative rings, and properties of such sequences are investigated. In particular we are concerned with two kinds of Fibonacci sequences of generalized quaternions over finite fields Fp, with p an odd prime, and their periods.