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>  Docs Center  >  IDL Reference  >  Advanced Math and Stats  >  IMSL Routines for Special Functions

### IMSL Routines for Special Functions

IMSL Routines for Special Functions

## Error Functions

IMSL_BETA: Beta function.

IMSL_BETAI: Incomplete beta function.

IMSL_ERF: Error function.

IMSL_ERFC: Complementary error function.

IMSL_LNBETA: Logarithmic beta function.

## Gamma Functions

IMSL_GAMMAI: Incomplete gamma function.

IMSL_LNGAMMA: Logarithmic gamma function.

## Bessel Functions with Real Order and Complex Argument

IMSL_BESSI: Modified Bessel function of the first kind.

IMSL_BESSI_EXP: Bessel function e-|x|I0(x), Bessel function e-|x|I1.

IMSL_BESSJ: Bessel function of the first kind.

IMSL_BESSK: Modified Bessel function of the second kind.

IMSL_BESSK_EXP: Bessel function exK0(x), Bessel function exK1(x).

IMSL_BESSY: Bessel function of the second kind.

## Elliptic Integrals

IMSL_ELE: Complete elliptic integral of the second kind.

IMSL_ELK: Complete elliptic integral of the first kind.

IMSL_ELRC: Special case of Carlson's elliptic integral.

IMSL_ELRD: Carlson’s elliptic integral of the second kind.

IMSL_ELRF: Carlson’s elliptic integral of the first kind.

IMSL_ELRJ: Carlson's elliptic integral of the third kind.

## Fresnel Integrals

IMSL_FRESNEL_COSINE: Cosine Fresnel integral.

IMSL_FRESNEL_SINE: Sine Fresnel integral.

## Airy Functions

IMSL_AIRY_AI: Airy function, and derivative of the Airy function.

IMSL_AIRY_BI: Airy function of the second find, and derivative of the Airy function of the second kind.

## Kelvin Functions

IMSL_KELVIN_BEI0: Kelvin function bei of the first kind, order 0, and derivative of the Kelvin function bei.

IMSL_KELVIN_BER0: Kelvin function ber of the first kind, order 0, and derivative of the Kelvin function ber.

IMSL_KELVIN_KEI0: Kelvin function kei of the second kind, order 0 and derivative of the Kelvin function kei.

IMSL_KELVIN_KER0: Kelvin function ker of the second kind, order 0, and derivative of the Kelvin function ker.

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