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Apéry-like sequences defined by four-term recurrence relations
Shaun Cooper
The Apéry numbers may be defined by a cubic three-term recurrence relation, that is, a three-term relation where the coefficients are polynomials in the index of degree . In thi…
Hypergeometric modular equations
Shaun Cooper, Wadim Zudilin
We record functional identities that, apart from being amazingly amusing by themselves, find applications in derivation of Ramanujan-…
Analogues of the Ramanujan--Mordell Theorem
Shaun Cooper, Ben Kane, Dongxi Ye
The Ramanujan--Mordell Theorem for sums of an even number of squares is extended to other quadratic forms and quadratic polynomials.
Crouching AGM, Hidden Modularity
Shaun Cooper, Jesús Guillera, Armin Straub +1
Special arithmetic series , whose coefficients are normally given as certain binomial sums, satisfy "self-replicating" functional identities.…
Holonomic alchemy and series for
Shaun Cooper, James G. Wan, Wadim Zudilin
We adopt the "translation" as well as other techniques to express several identities conjectured by Z.-W. Sun in arXiv:1102.5649v47 by means of known formulas for involving D…