Infinite summation and product identity

Key Points

• To investigate the identity involving infinite summation and product under the condition |t|>1.
• Analysis of mathematical series.
• Derivation of identities related to products and sums.
• Examination of convergence criteria.
• Establishment of a new identity for infinite summations and products.
• Demonstration of conditions under which the identity holds.
• Insights into the usage of series beyond typical convergence scenarios.