IMSL C Math Library
Chapter 9: 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