Ramanujan summation

Target entity: Ramanujan summation
Context triple: [theory of divergent series, usesConcept, Ramanujan summation]

• A. Ramanujan’s sum
  Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
• B. Cesàro summation
  Cesàro summation is a method of assigning finite values to certain divergent series by averaging their partial sums.
• C. Euler–Maclaurin summation formula
  The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
• D. Abel summation
  Abel summation is a method in mathematical analysis for assigning values to certain divergent series by considering the limit of their power series as the variable approaches 1 from below.
• E. Ramanujan tau function
  The Ramanujan tau function is a multiplicative arithmetic function arising from the Fourier coefficients of a modular discriminant form, central to the study of modular forms and number theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Ramanujan summation
Target entity description: Ramanujan summation is a technique in mathematical analysis that assigns finite values to certain divergent series in a way consistent with analytic continuation and other regularization methods.

• A. Ramanujan’s sum
  Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
• B. Cesàro summation
  Cesàro summation is a method of assigning finite values to certain divergent series by averaging their partial sums.
• C. Euler–Maclaurin summation formula
  The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
• D. Abel summation
  Abel summation is a method in mathematical analysis for assigning values to certain divergent series by considering the limit of their power series as the variable approaches 1 from below.
• E. Ramanujan tau function
  The Ramanujan tau function is a multiplicative arithmetic function arising from the Fourier coefficients of a modular discriminant form, central to the study of modular forms and number theory.
• F. None of above. chosen