Bessel function of the first kind

Bessel functions occur as the solution to specific differential equations. They are described with reference to a parameter known as the order, shown as a subscript. For integer orders Bessel functions can be represented as an infinite series. Order 0 and Order 1 expansions are shown here. The graph of a Bessel function is similar to a dampening sine wave. Usage in spatial analysis arises in connection with directional statistics and spline curve fitting. See the Mathworld website entry for more details

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Exponential integral function, E₁(x)

A definite integral function. Used in association with spline curve fitting. See the Mathworld website entry for more details

Gamma function, Γ

A widely used definite integral function. For integer values of x:

Γ(x)=(x‑1)! and Γ(x/2)=(x/2‑1)! so Γ(3/2)=(1/2)!/2=(Öπ)/2

See the Mathworld website entry for more details