Can Riemann's Analytic Continuation Solve My Reimann Zeta Function Error?

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SUMMARY

The discussion focuses on the implementation of Riemann's Analytic Continuation to resolve issues with calculating the Riemann Zeta Function in a C++ program. The user reports that their current implementation only yields correct results for values where the real part, 'a', is greater than 1. They seek guidance on applying Analytic Continuation to extend the function's validity across all complex numbers except for 1. References to series representations that converge globally are provided as potential solutions.

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  • Understanding of C++ programming language
  • Familiarity with complex analysis concepts
  • Knowledge of the Riemann Zeta Function
  • Experience with numerical methods for function evaluation
NEXT STEPS
  • Research Riemann's Analytic Continuation techniques
  • Explore series representations of the Riemann Zeta Function
  • Learn about convergence criteria for complex functions
  • Investigate numerical libraries in C++ for complex number calculations
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Mathematicians, C++ developers, and researchers working on complex analysis or numerical methods for evaluating special functions.

cmcraes
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I am currently writing a c++ program to calculate the Value of the Reimann Zeta Function, The problem is At the state its at, when you input a number a + bi it only gives the correct answer to values of a > 1. Can anyone show or link me Riemann's Analytic continuation of the Function so it works for all values? (Except 1 of course)
Thanks!
(If you want to see the code go here: http://www.cplusplus.com/forum/windows/129970/)
 
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