S Chapter Contents (PDF version)
S Chapter Introduction
NAG Library Manual

NAG Library Chapter Contents

S – Approximations of Special Functions

S Chapter Introduction

Routine
Name		 Mark of
Introduction
Purpose
S01BAF
Example Text
Example Data		 14 ln1+x
S01EAF
Example Text
Example Data		 14 Complex exponential, ez
S07AAF
Example Text
Example Data		 1 tan⁡x
S09AAF
Example Text
Example Data		 1 arcsin⁡x
S09ABF
Example Text
Example Data		 3 arccos⁡x
S10AAF
Example Text
Example Data		 3 tanh⁡x
S10ABF
Example Text
Example Data		 4 sinh⁡x
S10ACF
Example Text
Example Data		 4 cosh⁡x
S11AAF
Example Text
Example Data		 4 arctanh⁡x
S11ABF
Example Text
Example Data		 4 arcsinh⁡x
S11ACF
Example Text
Example Data		 4 arccosh⁡x
S13AAF
Example Text
Example Data
Example Plot		 1 Exponential integral E1x
S13ACF
Example Text
Example Data		 2 Cosine integral Cix
S13ADF
Example Text
Example Data		 5 Sine integral Six
S14AAF
Example Text
Example Data		 1 Gamma function
S14ABF
Example Text
Example Data		 8 Log gamma function
S14ACF
Example Text
Example Data		 14 ψx-ln⁡x
S14ADF
Example Text
Example Data		 14 Scaled derivatives of ψx
S14AEF
Example Text
Example Data		 20 Polygamma function ψnx for realx
S14AFF
Example Text
Example Data		 20 Polygamma function ψnz for complex z
S14AGF
Example Text
Example Data		 21 Logarithm of the gamma function ln⁡Γz
S14BAF
Example Text
Example Data		 14 Incomplete gamma functions Pa,x and Qa,x
S15ABF
Example Text
Example Data		 3 Cumulative Normal distribution function Px
S15ACF
Example Text
Example Data		 4 Complement of cumulative Normal distribution function Qx
S15ADF
Example Text
Example Data		 4 Complement of error function erfcx
S15AEF
Example Text
Example Data		 4 Error function erfx
S15AFF
Example Text
Example Data		 7 Dawson's integral
S15AGF
Example Text
Example Data		 22 Scaled complement of error function, erfcxx
S15DDF
Example Text
Example Data		 14 Scaled complex complement of error function, exp-z2erfc-iz
S17ACF
Example Text
Example Data		 1 Bessel function Y0x
S17ADF
Example Text
Example Data		 1 Bessel function Y1x
S17AEF
Example Text
Example Data		 5 Bessel function J0x
S17AFF
Example Text
Example Data		 5 Bessel function J1x
S17AGF
Example Text
Example Data		 8 Airy function Aix
S17AHF
Example Text
Example Data		 8 Airy function Bix
S17AJF
Example Text
Example Data		 8 Airy function Ai′x
S17AKF
Example Text
Example Data		 8 Airy function Bi′x
S17ALF
Example Text
Example Data		 20 Zeros of Bessel functions Jαx, Jα′x, Yαx or Yα′x
S17DCF
Example Text
Example Data		 13 Bessel functions Yν+az, reala≥0, complex z, ν=0,1,2,…
S17DEF
Example Text
Example Data		 13 Bessel functions Jν+az, reala≥0, complex z, ν=0,1,2,…
S17DGF
Example Text
Example Data		 13 Airy functions Aiz and Ai′z, complex z
S17DHF
Example Text
Example Data		 13 Airy functions Biz and Bi′z, complex z
S17DLF
Example Text
Example Data		 13 Hankel functions Hν+ajz, j=1,2, reala≥0, complex z, ν=0,1,2,…
S18ACF
Example Text
Example Data		 1 Modified Bessel function K0x
S18ADF
Example Text
Example Data		 1 Modified Bessel function K1x
S18AEF
Example Text
Example Data		 5 Modified Bessel function I0x
S18AFF
Example Text
Example Data		 5 Modified Bessel function I1x
S18CCF
Example Text
Example Data		 10 Scaled modified Bessel function exK0x
S18CDF
Example Text
Example Data		 10 Scaled modified Bessel function exK1x
S18CEF
Example Text
Example Data		 10 Scaled modified Bessel function e-xI0x
S18CFF
Example Text
Example Data		 10 Scaled modified Bessel function e-xI1x
S18DCF
Example Text
Example Data		 13 Modified Bessel functions Kν+az, reala≥0, complex z, ν=0,1,2,…
S18DEF
Example Text
Example Data		 13 Modified Bessel functions Iν+az, reala≥0, complex z, ν=0,1,2,…
S18GKF
Example Text
Example Data		 21 Bessel function of the 1st kind Jα±nz
S19AAF
Example Text
Example Data		 11 Kelvin function ber⁡x
S19ABF
Example Text
Example Data		 11 Kelvin function bei⁡x
S19ACF
Example Text
Example Data		 11 Kelvin function ker⁡x
S19ADF
Example Text
Example Data		 11 Kelvin function kei⁡x
S20ACF
Example Text
Example Data		 5 Fresnel integral Sx
S20ADF
Example Text
Example Data		 5 Fresnel integral Cx
S21BAF
Example Text		 8 Degenerate symmetrised elliptic integral of 1st kind RCx,y
S21BBF
Example Text		 8 Symmetrised elliptic integral of 1st kind RFx,y,z
S21BCF
Example Text		 8 Symmetrised elliptic integral of 2nd kind RDx,y,z
S21BDF
Example Text		 8 Symmetrised elliptic integral of 3rd kind RJx,y,z,r
S21BEF
Example Text		 22 Elliptic integral of 1st kind, Legendre form, Fϕ|m
S21BFF
Example Text		 22 Elliptic integral of 2nd kind, Legendre form, Eϕ|m
S21BGF
Example Text		 22 Elliptic integral of 3rd kind, Legendre form, Πn;ϕ|m
S21BHF
Example Text		 22 Complete elliptic integral of 1st kind, Legendre form, Km
S21BJF
Example Text		 22 Complete elliptic integral of 2nd kind, Legendre form, Em
S21CAF
Example Text
Example Data		 15 Jacobian elliptic functions sn, cn and dn of real argument
S21CBF
Example Text
Example Data		 20 Jacobian elliptic functions sn, cn and dn of complex argument
S21CCF
Example Text
Example Data		 20 Jacobian theta functions θkx,q of real argument
S21DAF
Example Text
Example Data		 20 General elliptic integral of 2nd kind Fz,k′,a,b of complex argument
S22AAF
Example Text
Example Data		 20 Legendre functions of 1st kind Pnmx or Pnm¯x
S30AAF
Example Text
Example Data		 22 Black–Scholes–Merton option pricing formula
S30ABF
Example Text
Example Data		 22 Black–Scholes–Merton option pricing formula with Greeks
S30BAF
Example Text
Example Data		 22 Floating-strike lookback option pricing formula
S30BBF
Example Text
Example Data		 22 Floating-strike lookback option pricing formula with Greeks
S30CAF
Example Text
Example Data		 22 Binary option: cash-or-nothing pricing formula
S30CBF
Example Text
Example Data		 22 Binary option: cash-or-nothing pricing formula with Greeks
S30CCF
Example Text
Example Data		 22 Binary option: asset-or-nothing pricing formula
S30CDF
Example Text
Example Data		 22 Binary option: asset-or-nothing pricing formula with Greeks
S30FAF
Example Text
Example Data		 22 Standard barrier option pricing formula
S30JAF
Example Text
Example Data		 22 Jump-diffusion, Merton's model, option pricing formula
S30JBF
Example Text
Example Data		 22 Jump-diffusion, Merton's model, option pricing formula with Greeks
S30NAF
Example Text
Example Data		 22 Heston's model option pricing formula
S30QCF
Example Text
Example Data		 22 American option: Bjerksund and Stensland pricing formula
S30SAF
Example Text
Example Data		 22 Asian option: geometric continuous average rate pricing formula
S30SBF
Example Text
Example Data		 22 Asian option: geometric continuous average rate pricing formula with Greeks
S Chapter Contents (PDF version)
S Chapter Introduction
NAG Library Manual
© The Numerical Algorithms Group Ltd, Oxford, UK. 2009