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