Tutorials¤

Lessons that take you through a complete piece of work, step by step. Start here if you are new to spexial and want to learn how it fits together rather than look something up.

Every step shows its output, and the output is real — these pages are executed as tests on every commit, so they cannot silently rot.

• Compute the Stefan–Boltzmann constant — evaluate \(\zeta(4)\) and the polylogarithm, check them against each other and against a closed form, and end with a physical constant matching every published digit. Covers double precision, jax.grad and jax.jit.
• Check Gegenbauer orthogonality by quadrature — evaluate a polynomial family across a whole grid at once, build a quadrature rule, and recover an identity matrix to machine precision. Covers array-valued evaluation, static arguments and jax.vmap.

If you already know what you are trying to accomplish, the how-to guides will get you there faster.