y1f(3)

y1f3

Bessel functions of first and second kind

Part of j0(3).

Usage

#include <math.h>

double

j0(double x);

float

j0f(float x);

double

j1(double x);

float

j1f(float x);

double

jn(int n, double x);

float

jnf(int n, float x);

double

y0(double x);

float

y0f(float x);

double

y1(double x);

float

y1f(float x);

double

yn(int n, double x);

float

ynf(int n, float x);

Library

Math Library (libm, -lm)

Overview

The functions j0(), j0f(), j1(), and j1f() compute the Bessel function of the first kind of orders 0 and 1 for the real value x; the functions jn() and jnf() compute the Bessel function of the first kind of the integer order n for the real value x.

The functions y0(), y0f(), y1(), and y1f() compute the linearly independent Bessel function of the second kind of orders 0 and 1 for the positive real value x; the functions yn() and ynf() compute the Bessel function of the second kind for the integer order n for the positive real value x.

Return values

These routines return values of their respective Bessel functions. For large positive inputs, they may underflow and return 0.

The following applies to y0(), y0f(), y1(), y1f(), yn(), and ynf(). If x is negative, including -, these routines will generate an invalid exception and return . If x is 0, these routines will generate a divide-by-zero exception and return -. If x is a sufficiently small positive number, then y1(), y1f(), yn(), and ynf() will generate an overflow exception and return -.

Releases

83 releases since FreeBSD 2.2.2-RELEASE; the text changed 44 times.

  1. 2.2.2–2.2.8
  2. 2.2.9
  3. 3.0–3.2
  4. 3.3–3.4
  5. 3.5–3.5.1
  6. 4.0–4.3
  7. 4.4
  8. 4.5–4.11
  9. 5.0–5.3
  10. 5.4–5.5
  11. 6.0–6.2
  12. 6.3
  13. 6.4
  14. 7.0
  15. 7.1
  16. 7.2
  17. 7.3
  18. 7.4
  19. 8.0
  20. 8.1
  21. 8.2
  22. 8.3
  23. 8.4
  24. 9.0
  25. 9.1
  26. 9.2
  27. 9.3
  28. 10.0
  29. 10.1
  30. 10.2
  31. 10.3
  32. 10.4
  33. 11.0
  34. 11.1
  35. 11.2
  36. 11.3
  37. 11.4
  38. 12.0
  39. 12.1
  40. 12.2
  41. 12.3
  42. 12.4
  43. 13.0–13.2
  44. 13.3–14.5
  45. 15.0–16.0

Standards

The j0(), j1(), jn(), y0(), y1(), and yn() functions conform to IEEE Std 1003.1-2001 (“POSIX.1”). The float versions are extensions.

History

This set of functions appeared in Version 7 AT&T UNIX.

From base 16.0-CURRENT-20261027-61c70dc16a79 in FreeBSD 16.0-CURRENT (2026-10-27). Parsed by carta from the page's mdoc source.