Explanation¤

Background on why spexial behaves the way it does. These pages are for reading away from the keyboard; nothing here is needed to get work done, and everything here is needed to predict what the library will do at its edges.

• About precision — why double precision is not optional for these functions, why it is a global switch, and how a computation silently ends up in float32 anyway.
• About domain edges, nan, and gradients that lie — why traced code returns nan instead of raising, why accuracy degrades near a pole, and why a gradient can be finite and still wrong.
• Why spexial exists alongside jax.scipy.special — what upstream can and cannot accept, the version-floor problem, and how this package is designed to shrink.
• About the algorithms — series orders, cross-over points, why the limit is usually cancellation rather than truncation, and what machine precision would actually cost.