The KELVIN_KERO function evaluates the Kelvin function of the second kind, ker, of order zero.

This routine requires an IDL Advanced Math and Stats license. For more information, contact your sales or technical support representative.

The modified Kelvin function ker₀(x) is defined to be ¬K₀(xe^pi/4). The Bessel function K₀(x) is defined:

If the keyword DERIVATIVE is set, the function ker₀′(x) is defined to be:

If x < 0, NaN (Not a Number) is returned. If x ≥ 119, then zero is returned.

The IMSL_KELVIN_KER0 function is based on the work of Burgoyne (1963).

Example

---

In this example, ker₀(0.4) and ker₀′(0.6) are evaluated.

PRINT, IMSL_KELVIN_KER0(0.4)

  1.06262

PRINT, IMSL_KELVIN_KER0(0.6, /DERIVATIVE)

  -1.45654

Syntax

---

Result = IMSL_KELVIN_KER0(X [, DERIVATIVE=value] [, /DOUBLE])

Return Value

---

The value of the Kelvin function of the second kind, ker, of order zero evaluated at x.

Arguments

---

X

Argument for which the function value is desired.

Keywords

---

DERIVATIVE (optional)

If present and nonzero, then the derivative of the Kelvin function of the second kind, ker, of order zero evaluated at x is computed.

DOUBLE (optional)

If present and nonzero, then double precision is used.

Version History

---

6.4	Introduced

See Also

---

IMSL_KELVIN_BEI0, IMSL_KELVIN_BER0, IMSL_KELVIN_KEI0