Special Functions

CNLMath : Special Functions

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, erf_inverse

Evaluates inverse complementary error function, erfc_inverse

Evaluates beta function, beta

Evaluates logarithmic beta function, log_beta

Evaluates incomplete beta function, beta_incomplete

Gamma Functions

Evaluates gamma function, gamma

Evaluates logarithmic gamma function, log_gamma

Evaluates incomplete gamma function, gamma_incomplete

Psi Function

Evaluates the derivative of the log gamma function, psi

Evaluates the real psi1 function, ψ1(x), psi1

Bessel Functions

Evaluates function J0, bessel_J0

Evaluates function J1, bessel_J1

Evaluates function Jn, bessel_Jx

Evaluates function Y0, bessel_Y0

Evaluates function Y1, bessel_Y1

Evaluates function Yv, bessel_Yx

Evaluates function I0, bessel_I0

Evaluates function e-|x|I0(x), bessel_exp_I0

Evaluates function I1, bessel_I1

Evaluates function e-|x|I1(x), bessel_exp_I1

Evaluates function Iv, bessel_Ix

Evaluates function K0, bessel_K0

Evaluates function exK0(x), bessel_exp_K0

Evaluates function K1, bessel_K1

Evaluates function exK1(x), bessel_exp_K1

Evaluates function Kv, bessel_Kx

Elliptic Integrals

Evaluates complete elliptic integral of the first kind, elliptic_integral_K

Evaluates complete elliptic integral of the second kind, elliptic_integral_E

Evaluates Carlson's elliptic integral of the first kind, elliptic_integral_RF

Evaluates Carlson's elliptic integral of the second kind, elliptic_integral_RD

Evaluates Carlson's elliptic integral of the third kind, elliptic_integral_RJ

Evaluates special case of Carlson's elliptic integral, elliptic_integral_RC

Fresnel Integrals

Evaluates cosine Fresnel integral, fresnel_integral_C

Evaluates sine Fresnel integral, fresnel_integral_S

Airy Functions

Evaluates Airy function, airy_Ai

Evaluates Airy function of the second kind, airy_Bi

Evaluates derivative of the Airy function, airy_Ai_derivative

Evaluates derivative of the Airy function of the second kind, airy_Bi_derivative

Kelvin Functions

Evaluates Kelvin function ber of the first kind order 0, kelvin_ber0

Evaluates Kelvin function bei of the first kind order 0, kelvin_bei0

Evaluates Kelvin function ker of the second kind order 0, kelvin_ker0

Evaluates Kelvin function kei of the second kind order 0, kelvin_kei0

Evaluates derivative of the Kelvin function ber, kelvin_ber0_derivative

Evaluates derivative of the Kelvin function bei, kelvin_bei0_derivative

Evaluates derivative of the Kelvin function ker, kelvin_ker0_derivative

Evaluates derivative of the Kelvin function kei, kelvin_kei0_derivative

Statistical Functions

Evaluates normal (Gaussian) distribution function, normal_cdf

Evaluates inverse normal distribution function, normal_inverse_cdf

Evaluates chi-squared distribution function, chi_squared_cdf

Evaluates Inverse chi-squared distribution function, chi_squared_inverse_cdf

Evaluates F distribution function, F_cdf

Evaluates inverse F distribution function, F_inverse_cdf

Evaluates student’s t distribution function, t_cdf

Evaluates inverse of the Student’s t distribution function, t_inverse_cdf

Evaluates gamma distribution function, gamma_cdf

Evaluates binomial distribution function, binomial_cdf

Evaluates hypergeometric distribution function, hypergeometric_cdf

Evaluates Poisson distribution function, poisson_cdf

Evaluates beta distribution function, beta_cdf

Evaluates inverse beta distribution function, beta_inverse_cdf

Evaluates bivariate normal distribution function, bivariate_normal_cdf

Basic Financial Functions

Evaluates cumulative interest, cumulative_interest

Evaluates cumulative principal, cumulative_principal

Evaluates depreciation using the fixed-declining method, depreciation_db

Evaluates depreciation using the double-declining method, depreciation_ddb

Evaluates depreciation using the straight-line method, depreciation_sln

Evaluates depreciation using the sum-of-years digits method, depreciation_syd

Evaluates depreciation using the variable declining method, depreciation_vdb

Evaluates and converts fractional price to decimal price, dollar_decimal

Evaluates and converts decimal price to fractional price, dollar_fraction

Evaluates effective rate, effective_rate

Evaluates future value, future_value

Evaluates future value considering a schedule of
compound interest rates, future_value_schedule

Evaluates interest payment, interest_payment

Evaluates interest rate, interest_rate_annuity

Evaluates internal rate of return, internal_rate_of_return

Evaluates internal rate of return for a schedule of cash flows, internal_rate_schedule

Evaluates modified internal rate, modified_internal_rate

Evaluates net present value, net_present_value

Evaluates nominal rate, nominal_rate

Evaluates number of periods, number_of_periods

Evaluates periodic payment, payment

Evaluates present value, present_value

Evaluates present value for a schedule of cash flows, present_value_schedule

Evaluates the payment for a principal, principal_payment

Bond Functions

Evaluates accrued interest at maturity, accr_interest_maturity

Evaluates accrued interest periodically, accr_interest_periodic

Evaluates bond-equivalent yield, bond_equivalent_yield

Evaluates convexity, convexity

Evaluates days in coupon period, coupon_days

Evaluates number of coupons, coupon_number

Evaluates days before settlement, days_before_settlement

Evaluates days to next coupon date, days_to_next_coupon

Evaluates depreciation per accounting period, depreciation_amordegrc

Evaluates depreciation, depreciation_amorlinc

Evaluates discount price, discount_price

Evaluates discount rate, discount_rate

Evaluates yield for a discounted security, discount_yield

Evaluates duration, duration

Evaluates the interest rate of a security, interest_rate_security

Evaluates Macauley duration, modified_duration

Evaluates next coupon date, next_coupon_date

Evaluates previous coupon date, previous_coupon_date

Evaluates price per $100 face value periodically, price

Evaluates price per $100 face value at maturity, price_maturity

Evaluates amount received at maturity, received_maturity

Evaluates Treasury bill's price, treasury_bill_price

Evaluates Treasury bill's yield, treasury_bill_yield

Evaluates year fraction, year_fraction

Evaluates yield at maturity, yield_maturity

Evaluates yield periodically, yield_periodic