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

valuates 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

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