Struve Function Hₙ(x) Calculator

Enter the order n and argument x to evaluate the Struve function Hₙ(x) via its power series. The related Bessel function Jₙ(x) and a curve plot are shown too.

Input

Compute the special function Struve Hₙ(x) from the order n and argument x using a power-series evaluation.

Order n (integer from 0 to 20)

Enter the order of the Struve function as an integer.

Argument x

Enter the real value x at which to evaluate the function.

Result

H0(3)

0.5743061488

Order n

Argument x

Related Bessel function J0(3)

-0.2600519549

Curve of H0(x)

How it works

The Struve function Hₙ(x) is evaluated with the power series Σ (-1)ᵐ / (Γ(m+3/2) Γ(m+n+3/2)) · (x/2)^(2m+n+1).
Terms are updated by a recurrence and accumulated with compensated (Kahan) summation to reduce cancellation.
The gamma function is computed through a log-gamma based on the Lanczos approximation.
For comparison, the Bessel function Jₙ(x) is computed with an analogous power series.
The order n accepts integers from 0 to 20, and x accepts any real number.

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