Elementare $q$-Identitäten.

Summary

Summary: We survey some simple $q$-identities without making use of partition theory or Heine series. Our approach emphasizes the analogy with classical analysis and, as much as possible, we try to motivate our developments by starting with the most important classical formulas. To elucidate the fundamental ideas, we restrict ourselves to characteristic "normal cases" and emphasize aspects, that appear to be typical. In particular, we treat $q$-Hermite and $q$-Laguerre polynomials by our approach. I hope that the presentation chosen here contributes to making the theory simpler and more transparent.