Error Functions

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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

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IMSL_GAMMA_ADV: Real gamma function.

IMSL_GAMMAI: Incomplete gamma function.

IMSL_LNGAMMA: Logarithmic gamma function.

Bessel Functions with Real Order and Complex Argument

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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 e^xK₀(x), Bessel function e^xK₁(x).

IMSL_BESSY: Bessel function of the second kind.

Elliptic Integrals

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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

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IMSL_FRESNEL_COSINE: Cosine Fresnel integral.

IMSL_FRESNEL_SINE: Sine Fresnel integral.

Airy Functions

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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

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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.