CALGO 757

Algorithm 757.

Procedures:

• strvh0: Struve function $\mathbf{H}_0(x)$
• strvh1: Struve function $\mathbf{H}_1(x)$

Other CALGO 757 procedures not yet included in this module:

• abram0, abram1, abram2: Abramowitz functions $f_m(x) = \int_{0}^{\infty} t^m e^{-t^2 -\frac{x}{t}} \, dt, \, \text{for } m = 0, 1, 2$
• airygi: Modified Airy function $\mathrm{Gi}(x)$
• airyhi: Modified Airy function $\mathrm{Hi}(x)$
• airint: Integral of the Airy function $\mathrm{Ai}(x)$ from $0$ to $x$
• birint: Integral of the Airy function $\mathrm{Bi}(x)$ from $0$ to $x$
• j0int: Integral of the Bessel function $J_0(x)$ from $0$ to $x$
• y0int: Integral of the Bessel function $Y_0(x)$ from $0$ to $x$
• i0int: Integral of the modified Bessel function $I_0(x)$ from $0$ to $x$
• k0int: Integral of the modified Bessel function $K_0(x)$ from $0$ to $x$
• debye1, debye2, debye3, debye4: Debye functions $D_n(x) = \frac{n}{x^n} \int_{0}^{x} \frac{t^n}{e^t-1} \, dt, \, \text{for } n = 1, 2, 3, 4$
• strvl0: Modified Struve function $\mathbf{L}_0(x)$
• strvl1: Modified Struve function $\mathbf{L}_1(x)$
• i0ml0: Difference between the modified Bessel and Struve functions $I_0(x) - \mathbf{L}_0(x)$
• i1ml1: Difference between the modified Bessel and Struve functions $I_1(x) - \mathbf{L}_1(x)$
• synch1: Synchrotron radiation function $f_1(x) = x \int_{x}^{\infty} K_{5/3}(t) \, dt$
• synch2: Synchrotron radiation function $f_2(x) = x K_{2/3}(x)$
• tran02, tran03, ..., tran09: Transport integrals $J_n(x) = \int_{0}^{x} \frac{t^n e^t}{(e^t-1)^2} \, dt, \, \text{for } n = 2, 3, \ldots, 9$
• atnint: Inverse-tangent integral $\int_{0}^{x} \frac{\arctan t}{t} \, dt$
• clausn: Clausen's integral $-\int_{0}^{x} \ln{\lvert 2 \sin\frac{t}{2} \rvert} \, dt$
• exp3: $\int_{0}^{x} e^{-t^3} \, dt$
• goodst: $\int_{0}^{\infty} \frac{e^{-t^2}}{t + x} \, dt$
• lobach: Lobachevski's integral $-\int_{0}^{\infty} \log \lvert \cos t \rvert \, dt$
• strom: Stromgren's integral $\frac{15}{4 \pi^4} \int_{0}^{x} \frac{t^7 e^{2 t}}{(e^t - 1)^3} \, dt$

Author

Allan J. MacLeod

History

• 1996-01-23 - Allan J. MacLeod
  • Original code.
• 2000-06-13 - Allan J. MacLeod
  • F77 code distributed by ACM: https://calgo.acm.org/757.zip
• 2001-10-10 - Alan Miller
  • F90 code adaptation by Alan Miller: https://jblevins.org/mirror/amiller/toms757.zip
• 2025-07-27 - Rodrigo Castro (GitHub: rodpcastro)
  • Retained only the subroutines strvh0 and strvh1; additional subroutines will be included as required.
  • Replaced array constructor (/.../) by the less verbose [...].
  • Replaced dp (double precision) by wp (working precision).
  • Replaced EPSILON(0.0_dp) by eps_wp (CSF working precision machine epsilon).
  • Removed subroutine errprn that prints error messages, which are unnecessary for strvh0 and strvh1.

References

1. Allan J. MacLeod. 1996. Algorithm 757: MISCFUN, a software package to compute uncommon special functions. ACM Trans. Math. Softw. 22, 3 (Sept. 1996), 288–301. https://doi.org/10.1145/232826.232846