The IMSL_KELVIN_KEI0 function evaluates the Kelvin function of the second kind, kei, of order zero.

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The modified Kelvin function kei₀(x) is defined to be . The Bessel function K₀(x) is defined as:

If the keyword DERIVATIVE is set, the function kei₀′(x) is defined to be:

The IMSL_KELVIN_KEI0 function is based on the work of Burgoyne (1963). If x < 0, NaN (Not a Number) is returned. If x ≥ 119, zero is returned.

Example

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In this example, kei₀(0.4) and kei₀′(0.6) are evaluated.

PRINT, IMSL_KELVIN_KEI0(0.4)

  -0.703800

PRINT, IMSL_KELVIN_KEI0(0.6, /DERIVATIVE)

  0.348164

Syntax

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Result = IMSL_KELVIN_KEI0(X [, DERIVATIVE=value] [, /DOUBLE])

Return Value

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

Arguments

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X

Argument for which the function value is desired.

Keywords

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DERIVATIVE (optional)

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

DOUBLE (optional)

If present and nonzero, then double precision is used.

Version History

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6.4	Introduced

See Also

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IMSL_KELVIN_BEI0, IMSL_KELVIN_BER0, IMSL_KELVIN_KER0