Catalog of Functionality > IMSL Mathematics Toolkit > Special Functions
  

Special Functions
Error Functions
BETA
Beta function
BETAI
Incomplete beta function
ERF
Error function
ERFC
Complementary error function
ERFCE
Evaluates the exponentially scaled complementary error function
ERFE
Evaluates a scaled function related to ERFC(z)
LNBETA
Logarithmic beta function
Gamma Functions
GAMMA
Gamma function
LNGAMMA
Logarithmic gamma function
GAMMAI
Incomplete gamma function
Bessel Functions with Real Order and Complex Argument
BESSI
Modified Bessel function of the first kind
BESSJ
Bessel function of the first kind
BESSK
Modified Bessel function of the second kind
BESSY
Bessel function of the second kind
BESSI_EXP
Evaluates the exponentially scaled modified Bessel function of the first kind of orders zero and one.
BESSK_EXP
Evaluates the exponentially scaled modified Bessel function of the third kind of orders zero and one.
Elliptical Integrals
ELE
Evaluates the complete elliptic integral of the second kind E(x).
ELK
Evaluates the complete elliptic integral of the kind K(x).
ELRF
Evaluates Carlson's elliptic integral of the first kind RF(x, y, z).
ELRD
Evaluates Carlson's elliptic integral of the second kind RD(x, y, z).
ELRJ
Evaluates Carlson's elliptic integral of the third kind RJ (x, y, z, r)
ELRC
Evaluates an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.
Fresnel Integrals
FRESNEL_COSINE
Evaluates the cosine Fresnel integral.
FRESNEL_SINE
Evaluates the sine Fresnel integral.
Airy Functions
AIRY_AI
Evaluates the Airy function.
AIRY_BI
Evaluates the Airy function of the second kind.
Hermite Functions
HERMITE
Evaluates Hermite polynomials.
Kelvin Functions
KELVIN_BER0
Evaluates the Kelvin function of the first kind, ber, of order zero.
KELVIN_BEI0
Evaluates the Kelvin function of the first kind, bei, of order zero.
KELVIN_KER0
Evaluates the Kelvin function of the second kind, ker, of order zero.
KELVIN_KEI0
Evaluates the Kelvin function of the second kind, kei, of order zero.
Legendre Functions
LEGENDRE
Evaluates the associated Legendre functions.
Basic Financial Functions
CUM_INTR
Evaluates the cumulative interest paid between two periods.
CUM_PRINC
Evaluates the cumulative principal paid between two periods.
DEPRECIATION_DB
Evaluates the depreciation of an asset using the fixed-declining balance method.
DEPRECIATION_DDB
Evaluates the depreciation of an asset using the double-declining balance method.
DEPRECIATION_SLN
Evaluates the depreciation of an asset using the straight-line method.
DEPRECIATION_SYD
Evaluates the depreciation of an asset using the sum-of-years digits method.
DEPRECIATION_VDB
Evaluates the depreciation of an asset for any given period using the variable-declining balance method.
DOLLAR_DECIMAL
Converts a fractional price to a decimal price.
DOLLAR_FRACTION
Converts a decimal price to a fractional price.
EFFECTIVE_RATE
Evaluates effective annual interest rate.
FUTURE_VALUE
Evaluates the future value of an investment.
FUTURE_VAL_SCHD
Evaluates the future value of an initial principal taking into consideration a schedule of compound interest rates.
INT_PAYMENT
Evaluates the interest payment for an investment for a given period.
INT_RATE_ANNUITY
Evaluates the interest rate per period of an annuity.
INT_RATE_RETURN
Evaluates the internal rate of return for a schedule of cash flows.
INT_RATE_SCHD
Evaluates the internal rate of return for a schedule of cash flows. It is not necessary that the cash flows be periodic.
MOD_INTERN_RATE
Evaluates the modified internal rate of return for a schedule of periodic cash flows.
NET_PRES_VALUE
Evaluates the net present value of a stream of unequal periodic cash flows, which are subject to a given discount rate.
NOMINAL_RATE
Evaluates the nominal annual interest rate.
NUM_PERIODS
Evaluates the number of periods for an investment for which periodic and constant payments are made and the interest rate is constant.
PAYMENT
Evaluates the periodic payment for an investment.
PRESENT_VALUE
Evaluates the net present value of a stream of equal periodic cash flows, which are subject to a given discount rate.
PRES_VAL_SCHD
Evaluates the present value for a schedule of cash flows. It is not necessary that the cash flows be periodic.
PRINC_PAYMENT
Evaluates the payment on the principal for a specified period.
Bond Functions
ACCR_INT_MAT
Evaluates the interest which has accrued on a security that pays interest at maturity.
ACCR_INT_PER
Evaluates the interest which has accrued on a security that pays interest periodically.
BOND_EQV_YIELD
Evaluates the bond-equivalent yield of a Treasury bill.
CONVEXITY
Evaluates the convexity for a security.
COUPON_DAYS
Evaluates the number of days in the coupon period containing the settlement date.
COUPON_NUM
Evaluates the number of coupons payable between the settlement date and the maturity date.
SETTLEMENT_DB
Evaluates the number of days starting with the beginning of the coupon period and ending with the settlement date.
COUPON_DNC
Evaluates the number of days starting with the settlement date and ending with the next coupon date.
DEPREC_AMORDEGRC
Evaluates the depreciation for each accounting period. During the evaluation of the function a depreciation coefficient based on the asset life is applied.
DEPREC_AMORLINC
Evaluates the depreciation for each accounting period.
DISCOUNT_PR
Evaluates the price of a security sold for less than its face value.
DISCOUNT_RT
Evaluates the interest rate implied when a security is sold for less than its value at maturity in lieu of interest payments.
DISCOUNT_YLD
Evaluates the annual yield of a discounted security.
DURATION
Evaluates the annual duration of a security, where the security has periodic interest payments.
INT_RATE_SEC
Evaluates the interest rate of a fully invested security.
DURATION_MAC
Evaluates the modified Macauley duration of a security.
COUPON_NCD
Evaluates the first coupon date which follows the settlement date.
COUPON_PCD
Evaluates the coupon date which immediately precedes the settlement date.
PRICE_PERIODIC
Evaluates the price, per $100 face value, of a security that pays periodic interest.
PRICE_MATURITY
Evaluates the price, per $100 face value, of a security that pays interest at maturity.
MATURITY_REC
Evaluates the amount one receives when a fully invested security reaches the maturity date.
TBILL_PRICE
Evaluates the price per $100 face value of a Treasury bill.
TBILL_YIELD
Evaluates the yield of a Treasury bill.
YEAR_FRACTION
Evaluates the fraction of a year represented by the number of whole days between two dates.
YIELD_MATURITY
Evaluates the annual yield of a security that pays interest at maturity.
YIELD_PERIODIC
Evaluates the yield of a security that pays periodic interest.

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