11. It is quite common for different mock theta functions to have the same shadow. 12. The proof involves index theory and certain subtle properties of the Jacobi theta functions . 13. The fundamental solution of the heat equation on a circle is called a theta function . 14. This method is very convenient for numerical calculation : the theta functions converge very quickly. 15. One important such use of Poisson summation concerns theta functions : periodic summations of Gaussians. 16. The Jacobi theta function may be written in terms of the Ramanujan theta function as: 17. The Jacobi theta function may be written in terms of the Ramanujan theta function as: 18. The most common form of theta function is that occurring in the theory of elliptic functions. 19. Where is the-theta function . 20. In the field of elliptic functions he also published results concerning abelian integrals and theta functions .
