2 papers
math-ph2024
Extended Landen's formulas and double product theta functions
Kiyoshi Sogo
For an arbitrary positive integer , Landen's formula is extended to express theta function with modulus by product of theta functions with , which is applied to seve…
math-ph2024
Theory of general theta relations, addition formulas, and theta constants identities
Kiyoshi Sogo
Jacobi's theta relations among quartic products of theta functions are generalized to those of arbitrary products. Igusa's procedure of derivation is extended to prove such gen…