On a new modular equation of degree five and Eisenstein series identities of associated levels

In this research article, we obtain few theta function identities of level ten employing Ramanujan’s ${}_1{\psi }_1$ summation formula. Using these identities, we derive a new modular equation of degree five. Further, we establish Eisenstein series identities of level ten using Bailey’s very-well poised ${}_6{\psi }_6$ summation formula.