IMSL Mathematics Reference Guide > Special Functions
  

Special Functions
 
This section contains the following topics:
Error and Gamma Functions
*Error Functions
* ERF Function (PV-WAVE Advantage)—Error function.
* ERFCE Function (PV-WAVE Advantage)—Evaluates the exponentially scaled complementary error function.
* ERFE Function (PV-WAVE Advantage)—Evaluates a scaled function related to ERFC(z).
* ERFC Function (PV-WAVE Advantage)—Complementary error function.
* BETA Function (PV-WAVE Advantage)—Beta function.
* LNBETA Function (PV-WAVE Advantage)—Logarithmic beta function.
* BETAI Function (PV-WAVE Advantage)—Incomplete beta function.
*Gamma Functions
* GAMMA Function (PV-WAVE Advantage)—Gamma function.
* LNGAMMA Function (PV-WAVE Advantage)—Logarithmic gamma function.
* GAMMAI Function (PV-WAVE Advantage)—Incomplete gamma function.
*Bessel Functions with Real Order and Complex Argument
* BESSI Function (PV-WAVE Advantage)—Modified Bessel function of the first kind.
* BESSJ Function (PV-WAVE Advantage)—Bessel function of the first kind.
* BESSK Function (PV-WAVE Advantage)—Modified Bessel function of the second kind.
* BESSY Function (PV-WAVE Advantage)—Bessel function of the second kind.
* BESSI_EXP Function (PV-WAVE Advantage)—Bessel function e-|x|I0(x), Bessel function e-|x|I1(x).
* BESSK_EXP Function (PV-WAVE Advantage)—Bessel function exK0(x), Bessel function exK1(x).
Elliptic Integrals
* ELK Function (PV-WAVE Advantage)—Complete elliptic integral of the first kind.
* ELE Function (PV-WAVE Advantage)—Complete elliptic integral of the second kind.
* ELRF Function (PV-WAVE Advantage)—Carlson's elliptic integral of the first kind.
* ELRD Function (PV-WAVE Advantage)—Carlson's elliptic integral of the second kind.
* ELRJ Function (PV-WAVE Advantage)—Carlson's elliptic integral of the third kind.
* ELRC Function (PV-WAVE Advantage)—Special case of Carlson's elliptic integral.
Fresnel Integrals
* FRESNEL_COSINE Function (PV-WAVE Advantage)—Cosine Fresnel integral.
* FRESNEL_SINE Function (PV-WAVE Advantage)—Sine Fresnel integral.
Airy Functions
* AIRY_AI Function (PV-WAVE Advantage)—Airy function, and derivative of the Airy function.
* AIRY_BI Function (PV-WAVE Advantage)—Airy function of the second find, and derivative of the Airy function of the second kind.
Hermite Functions:
* HERMITE Function (PV-WAVE Advantage)—Evaluates Hermite polynomials.
Kelvin Functions
* KELVIN_BER0 Function (PV-WAVE Advantage)—Kelvin function ber of the first kind, order 0, and derivative of the Kelvin function ber.
* KELVIN_BEI0 Function (PV-WAVE Advantage)—Kelvin function bei of the first kind, order 0, and derivative of the Kelvin function bei.
* KELVIN_KER0 Function (PV-WAVE Advantage)—Kelvin function ker of the second kind, order 0, and derivative of the Kelvin function ker.
* KELVIN_KEI0 Function (PV-WAVE Advantage)—Kelvin function kei of the second kind, order 0 and derivative of the Kelvin function kei.
Legendre Functions
* LEGENDRE Function (PV-WAVE Advantage)—Evaluates the associated Legendre functions.
Basic Financial Functions
* CUM_INTR Function (PV-WAVE Advantage)—Evaluates cumulative interest.
* CUM_PRINC Function (PV-WAVE Advantage)—Evaluates cumulative principal.
* DEPRECIATION_DB Function (PV-WAVE Advantage)—Evaluates depreciation using the fixed-declining method.
* DEPRECIATION_DDB Function (PV-WAVE Advantage)—Evaluates depreciation using the double-declining method.
* DEPRECIATION_SLN Function (PV-WAVE Advantage)—Evaluates depreciation using the straight-line method.
* DEPRECIATION_SYD Function (PV-WAVE Advantage)—Evaluates depreciation using the sum-of-years digits method.
* DEPRECIATION_VDB Function (PV-WAVE Advantage)—Evaluates depreciation using the variable declining method.
* DOLLAR_DECIMAL Function (PV-WAVE Advantage)—Evaluates and converts fractional price to decimal price.
* DOLLAR_FRACTION Function (PV-WAVE Advantage)—Evaluates and converts decimal price to fractional price.
* EFFECTIVE_RATE Function (PV-WAVE Advantage)—Evaluates effective rate.
* FUTURE_VALUE Function (PV-WAVE Advantage)—Evaluates future value.
* FUTURE_VAL_SCHD Function (PV-WAVE Advantage)—Evaluates future value; considering a schedule of compound interest rates.
* INT_PAYMENT Function (PV-WAVE Advantage)—Evaluates interest payment.
* INT_RATE_ANNUITY Function (PV-WAVE Advantage)—Evaluates interest rate.
* INT_RATE_RETURN Function (PV-WAVE Advantage)—Evaluates internal rate of return.
* INT_RATE_SCHD Function (PV-WAVE Advantage)—Evaluates internal rate of return for a schedule of cash flows.
* MOD_INTERN_RATE Function (PV-WAVE Advantage)—Evaluates modified internal rate.
* NET_PRES_VALUE Function (PV-WAVE Advantage)—Evaluates net present value.
* NOMINAL_RATE Function (PV-WAVE Advantage)—Evaluates nominal rate.
* NUM_PERIODS Function (PV-WAVE Advantage)—Evaluates number of periods.
* PAYMENT Function (PV-WAVE Advantage)—Evaluates periodic payment.
* PRESENT_VALUE Function (PV-WAVE Advantage)—Evaluates present value.
* PRES_VAL_SCHD Function (PV-WAVE Advantage)—Evaluates present value for a schedule of cash flows.
* PRINC_PAYMENT Function (PV-WAVE Advantage)—Evaluates the payment for a principal.
Bond Functions
* ACCR_INT_MAT Function (PV-WAVE Advantage)—Evaluates accrued interest at maturity.
* ACCR_INT_PER Function (PV-WAVE Advantage)—Evaluates accrued interest periodically.
* BOND_EQV_YIELD Function (PV-WAVE Advantage)—Evaluates bond-equivalent yield.
* CONVEXITY Function (PV-WAVE Advantage)—Evaluates convexity.
* COUPON_DAYS Function (PV-WAVE Advantage)—Evaluates days in a coupon period.
* COUPON_NUM Function (PV-WAVE Advantage)—Evaluates number of coupons.
* SETTLEMENT_DB Function (PV-WAVE Advantage)—Evaluates days before settlement.
* COUPON_DNC Function (PV-WAVE Advantage)—Evaluates days to next coupon date.
* DEPREC_AMORDEGRC Function (PV-WAVE Advantage)—Evaluates depreciation per accounting period .
* DEPREC_AMORLINC Function (PV-WAVE Advantage)—Evaluates depreciation.
* DISCOUNT_PR Function (PV-WAVE Advantage)—Evaluates discount price.
* DISCOUNT_RT Function (PV-WAVE Advantage)—Evaluates discount rate.
* DISCOUNT_YLD Function (PV-WAVE Advantage)—Evaluates yield for a discounted security.
* DURATION Function (PV-WAVE Advantage)—Evaluates duration.
* INT_RATE_SEC Function (PV-WAVE Advantage)—Evaluates the interest rate of a security.
* DURATION_MAC Function (PV-WAVE Advantage)—Evaluates Macauley duration.
* COUPON_NCD Function (PV-WAVE Advantage)—Evaluates next coupon date.
* COUPON_PCD Function (PV-WAVE Advantage)—Evaluates previous coupon date.
* PRICE_PERIODIC Function (PV-WAVE Advantage)—Evaluates price per $100 face value periodically.
* PRICE_MATURITY Function (PV-WAVE Advantage)—Evaluates price per $100 face value at maturity.
* MATURITY_REC Function (PV-WAVE Advantage)—Evaluates amount received at maturity.
* TBILL_PRICE Function (PV-WAVE Advantage)—Evaluates Treasury bill's price.
* TBILL_YIELD Function (PV-WAVE Advantage)—Evaluates Treasury bill's yield.
* YEAR_FRACTION Function (PV-WAVE Advantage)—Evaluates year fraction.
* YIELD_MATURITY Function (PV-WAVE Advantage)—Evaluates yield at maturity.
* YIELD_PERIODIC Function (PV-WAVE Advantage)—Evaluates yield periodically.

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