Euler’s identity for sine product

Target entity: Euler’s identity for sine product
Context triple: [Jacobi triple product, generalizes, Euler’s identity for sine product]

• A. Wallis product
  The Wallis product is an infinite product formula for π/2, discovered by John Wallis in the 17th century and notable as one of the earliest infinite product representations of π.
• B. Euler’s formula for complex exponentials
  Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
• C. Euler’s reflection formula
  Euler’s reflection formula is a fundamental identity in complex analysis that relates the values of the Gamma function at z and 1−z through the sine function, revealing a deep symmetry of the Gamma function.
• D. Euler product formula for the Riemann zeta function
  The Euler product formula for the Riemann zeta function is a fundamental identity in analytic number theory that expresses the zeta function as an infinite product over all prime numbers, revealing a deep connection between primes and the distribution of integers.
• E. Jacobi triple product
  The Jacobi triple product is a fundamental identity in number theory and complex analysis that expresses an infinite product as an infinite sum, playing a key role in the theory of theta functions and q-series.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Euler’s identity for sine product
Target entity description: Euler’s identity for sine product is a classical formula expressing the sine function as an infinite product, foundational in the theory of infinite products and special functions.

• A. Wallis product
  The Wallis product is an infinite product formula for π/2, discovered by John Wallis in the 17th century and notable as one of the earliest infinite product representations of π.
• B. Euler’s formula for complex exponentials
  Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
• C. Euler’s reflection formula
  Euler’s reflection formula is a fundamental identity in complex analysis that relates the values of the Gamma function at z and 1−z through the sine function, revealing a deep symmetry of the Gamma function.
• D. Euler product formula for the Riemann zeta function
  The Euler product formula for the Riemann zeta function is a fundamental identity in analytic number theory that expresses the zeta function as an infinite product over all prime numbers, revealing a deep connection between primes and the distribution of integers.
• E. Jacobi triple product
  The Jacobi triple product is a fundamental identity in number theory and complex analysis that expresses an infinite product as an infinite sum, playing a key role in the theory of theta functions and q-series.
• F. None of above. chosen