An elementary proof of Ramanujan's circular summation formula and its generalizations

DOI10.1007/s11139-011-9364-4zbMath1282.11040OpenAlexW2035431994MaRDI QIDQ427275

Ping Xu

Publication date: 13 June 2012

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-011-9364-4

zbMATH Keywords

elementary methodRamanujan's circular summationgeneralizations

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Elliptic functions and integrals (33E05)

Related Items (7)

SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES ⋮ Circular summation formulas for theta function \(\vartheta_4(z| \tau)\) ⋮ Some Ramanujan-type circular summation formulas ⋮ The \(t\)-coefficient method. III: A general series expansion for the product of theta functions with different bases and its applications. ⋮ Some new circular summation formulas of theta functions ⋮ Some extensions for Ramanujan's circular summation formulas and applications ⋮ A note for Ramanujan's circular summation formula

Cites Work

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• Circular summation of theta functions in Ramanujan's lost notebook
• On a new circular summation of theta functions
• A generalized circular summation of theta function and its application
• On the circular summation of the eleventh powers of Ramanujan's theta function
• On a result of Ramanujan on theta functions
• Circular summation of the 13th powers of Ramanujan's theta function
• Circular summations of theta functions in Ramanujan's lost notebook
• The root lattice $A^*_n$ and Ramanujan’s circular summation of theta functions
• Additive decompositions of θ-functions of multiple arguments
• Some Cubic Modular Identities of Ramanujan
• The sixth, eighth, ninth, and tenth powers of Ramanujan’s theta function

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