Special Functions

Functions

Error and Gamma Functions

Error Functions

Evaluates error function erf

Evaluates complementary error function erfc

Evaluates exponentially error function erfce

Evaluates scaled function erfe

Evaluates inverse error function erfInverse

Evaluates inverse complementary error function erfcInverse

Evaluates beta function beta

Evaluates logarithmic beta function logBeta

Evaluates incomplete beta function betaIncomplete

Gamma Functions

Evaluates gamma function gamma

Evaluates logarithmic gamma function logGamma

Evaluates incomplete gamma function gammaIncomplete

Psi Function

Evaluates the derivative of the log gamma function psi

Evaluates the real psi1 function, ψ1(x) psi1

Bessel Functions

Evaluates function J0 besselJ0

Evaluates function J1 besselJ1

Evaluates function Jn besselJx

Evaluates function Y0 besselY0

Evaluates function Y1 besselY1

Evaluates function Yv besselYx

Evaluates function I0 besselI0

Evaluates function e-|x|I0(x) besselExpI0

Evaluates function I1 besselI1

Evaluates function e-|x|I1(x) besselExpI1

Evaluates function Iv besselIx

Evaluates function K0 besselK0

Evaluates function exK0(x) besselExpK0

Evaluates function K1 besselK1

Evaluates function exK1(x) besselExpK1

Evaluates function Kv besselKx

Elliptic Integrals

Evaluates complete elliptic integral of the first kind ellipticIntegralK

Evaluates complete elliptic integral of the second kind ellipticIntegralE

Evaluates Carlson’s elliptic integral of the first kind ellipticIntegralRF

Evaluates Carlson’s elliptic integral of the second kind ellipticIntegralRD

Evaluates Carlson’s elliptic integral of the third kind ellipticIntegralRJ

Evaluates special case of Carlson’s elliptic integral ellipticIntegralRC

Fresnel Integrals

Evaluates cosine Fresnel integral fresnelIntegralC

Evaluates sine Fresnel integral fresnelIntegralS

Airy Functions

Evaluates Airy function airyAi

Evaluates Airy function of the second kind airyBi

Evaluates derivative of the Airy function airyAiDerivative

Evaluates derivative of the Airy function of the second kind airyBiDerivative

Kelvin Functions

Evaluates Kelvin function ber of the first kind order 0 kelvinBer0

Evaluates Kelvin function bei of the first kind order 0 kelvinBei0

Evaluates Kelvin function ker of the second kind order 0 kelvinKer0

Evaluates Kelvin function kei of the second kind order 0 kelvinKei0

Evaluates derivative of the Kelvin function ber kelvinBer0Derivative

Evaluates derivative of the Kelvin function bei kelvinBei0Derivative

Evaluates derivative of the Kelvin function ker kelvinKer0Derivative

Evaluates derivative of the Kelvin function kei kelvinKei0Derivative

Statistical Functions

Evaluates normal (Gaussian) distribution function normalCdf

Evaluates inverse normal distribution function normalInverseCdf

Evaluates chi-squared distribution function chiSquaredCdf

Evaluates Inverse chi-squared distribution function chiSquaredInverseCdf

Evaluates F distribution function fCdf

Evaluates inverse F distribution function fInverseCdf

Evaluates student’s t distribution function tCdf

Evaluates inverse of the Student’s t distribution function tInverseCdf

Evaluates gamma distribution function gammaCdf

Evaluates binomial distribution function binomialCdf

Evaluates hypergeometric distribution function hypergeometricCdf

Evaluates Poisson distribution function poissonCdf

Evaluates beta distribution function betaCdf

Evaluates inverse beta distribution function betaInverseCdf

Evaluates bivariate normal distribution function bivariateNormalCdf

Basic Financial Functions

Evaluates cumulative interest cumulativeInterest

Evaluates cumulative principal cumulativePrincipal

Evaluates depreciation using the fixed-declining method depreciationDb

Evaluates depreciation using the double-declining method depreciationDdb

Evaluates depreciation using the straight-line method depreciationSln

Evaluates depreciation using the sum-of-years digits method depreciationSyd

Evaluates depreciation using the variable declining method depreciationVdb

Evaluates and converts fractional price to decimal price dollarDecimal

Evaluates and converts decimal price to fractional price dollarFraction

Evaluates effective rate effectiveRate

Evaluates future value futureValue

Evaluates future value considering a schedule of

compound interest rates futureValueSchedule

Evaluates interest payment interestPayment

Evaluates interest rate interestRateAnnuity

Evaluates internal rate of return internalRateOfReturn

Evaluates internal rate of return for a schedule of cash flows internalRateSchedule

Evaluates modified internal rate modifiedInternalRate

Evaluates net present value netPresentValue

Evaluates nominal rate nominalRate

Evaluates number of periods numberOfPeriods

Evaluates periodic payment payment

Evaluates present value presentValue

Evaluates present value for a schedule of cash flows presentValueSchedule

Evaluates the payment for a principal principalPayment

Bond Functions

Evaluates accrued interest at maturity accrInterestMaturity

Evaluates accrued interest periodically accrInterestPeriodic

Evaluates bond-equivalent yield bondEquivalentYield

Evaluates convexity convexity

Evaluates days in coupon period couponDays

Evaluates number of coupons couponNumber

Evaluates days before settlement daysBeforeSettlement

Evaluates days to next coupon date daysToNextCoupon

Evaluates depreciation per accounting period depreciationAmordegrc

Evaluates depreciation depreciationAmorlinc

Evaluates discount price discountPrice

Evaluates discount rate discountRate

Evaluates yield for a discounted security discountYield

Evaluates duration duration

Evaluates the interest rate of a security interestRateSecurity

Evaluates Macauley duration modifiedDuration

Evaluates next coupon date nextCouponDate

Evaluates previous coupon date previousCouponDate

Evaluates price per $100 face value periodically price

Evaluates price per $100 face value at maturity priceMaturity

Evaluates amount received at maturity receivedMaturity

Evaluates Treasury bill’s price treasuryBillPrice

Evaluates Treasury bill’s yield treasuryBillYield

Evaluates year fraction yearFraction

Evaluates yield at maturity yieldMaturity

Evaluates yield periodically yieldPeriodic