Modified Struve Function Lₙ(x) Calculator

Enter the order n and x to compute the modified Struve function Lₙ(x) via its series expansion, with a graph.

Input

Compute the modified Struve function Lₙ(x) from its series expansion. Enter the order n and the argument x.

Order n

A real number ≥ 0 (e.g. 0, 1, 2)

Argument x

Enter a real number (e.g. 1, 2.5, -1)

Value of L0(1)

0.7102431859

Order n

Input x

Graph of Lₙ(x)

The modified Struve function Lₙ(x) is defined by the series Lₙ(x) = Σ (x/2)^(2m+n+1) / (Γ(m+3/2)·Γ(m+n+3/2)).
This tool evaluates the leading term with a log-gamma (Lanczos) approximation and accumulates later terms via the ratio between successive terms.
The order n accepts any real value ≥ 0, and x accepts any real value. Lₙ(x) grows rapidly for large x.
Results are computed near double precision. For extremely large inputs, overflow may reduce accuracy.

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