On the algebraic relations and dissections for certain continued fractions of order 104

Key Points

• The research aims to explore algebraic relations for continued fractions and their dissections.
• Derivation of thirteen special cases of Ramanujan's continued fractions
• Establishment of 2- and 4-dissections of continued fractions
• Connection of continued fractions with their respective reciprocals
• Validation of results relating to the established dissections
• Discovery of new coloured partition identities through algebraic relations