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Mathematical & Computational Physics

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Mathematical & Computational Physics

Bessel Functions

A family of canonical special functions J_α(x) and Y_α(x) serving as solutions to Bessel's differential equation.

x² y'' + x y' + (x² - α²) y = 0 ⇒ y(x) = A J_α(x) + B Y_α(x) Cylindrical Special Functions Mathematical & Computational Physics

Big O Notation

A mathematical notation classifying algorithms according to how their execution time or memory requirements grow as input size N increases.

f(N) = O(g(N)) if |f(N)| ≤ C |g(N)| for N ≥ N₀ Algorithmic Asymptotic Complexity Mathematical & Computational Physics

Boundary Value Problem

A differential equation together with a set of additional constraints, called boundary conditions, specified at the boundaries of the…

Dirichlet: y(a)=y_A; Neumann: y'(a)=y'_A; Robin: α y(a) + β y'(a) = γ Differential Equation Condition