Special Functions

Special Functions is an iOS tool for exploring special functions, aimed at teaching and researching mathematics, physics, and engineering. Supports four classic functions: Bessel, Legendre, Hermite, and Laguerre, with adjustable order n, to draw function curves, numerical derivatives, or overlay two orders for comparison. The Lab page allows for custom domain definition, preset teaching intervals, and verification of three recursive relationships at any sampling point. Zero points can be found using binary search, and the results can be easily copied for integration reference. The Analysis page can estimate the weighted inner product to test orthogonality when n ≠ m, and perform trapezoidal integration and zero based partition integration demonstrations. The Reference page summarizes differential equations, weight functions, recursive formulas, and physical backgrounds of various functions, and supports one click jump to Lab drawing.