Bailey pairs and quantum q-series identities. I. The classical identities

Key Points

• Quadratic forms play a crucial role in proving q-series identities, highlighting their mathematical relevance.
• The analysis specifically demonstrates relationships at roots of unity through established identities and lemmas.
• Approach utilizing Bailey pairs and changes-of-base enhances the derivation of identities in this context.
• Findings emphasize further exploration of Bailey pairs within the realm of infinite families and mock theta functions.