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 ln(1 + x)
S01EAF
Example Text
Example Data
14 Complex exponential, ez
S07AAF
Example Text
Example Data
1 tanx
S09AAF
Example Text
Example Data
1 arcsinx
S09ABF
Example Text
Example Data
3 arccosx
S10AAF
Example Text
Example Data
3 tanhx
S10ABF
Example Text
Example Data
4 sinhx
S10ACF
Example Text
Example Data
4 coshx
S11AAF
Example Text
Example Data
4 arctanhx
S11ABF
Example Text
Example Data
4 arcsinhx
S11ACF
Example Text
Example Data
4 arccoshx
S13AAF
Example Text
Example Data
Example Plot
1 Exponential integral E1(x)
S13ACF
Example Text
Example Data
2 Cosine integral Ci(x)
S13ADF
Example Text
Example Data
5 Sine integral Si(x)
S14AAF
Example Text
Example Data
1 Gamma function
S14ABF
Example Text
Example Data
8 Log gamma function
S14ACF
Example Text
Example Data
14 ψ(x) - lnx
S14ADF
Example Text
Example Data
14 Scaled derivatives of ψ(x)
S14AEF
Example Text
Example Data
20 Polygamma function ψ(n)(x) for realx
S14AFF
Example Text
Example Data
20 Polygamma function ψ(n)(z) for complex z
S14AGF
Example Text
Example Data
21 Logarithm of the gamma function lnΓ(z)
S14BAF
Example Text
Example Data
14 Incomplete gamma functions P(a,x) and Q(a,x)
S15ABF
Example Text
Example Data
3 Cumulative Normal distribution function P(x)
S15ACF
Example Text
Example Data
4 Complement of cumulative Normal distribution function Q(x)
S15ADF
Example Text
Example Data
4 Complement of error function erfc(x)
S15AEF
Example Text
Example Data
4 Error function erf(x)
S15AFF
Example Text
Example Data
7 Dawson's integral
S15AGF
Example Text
Example Data
22 Scaled complement of error function, erfcx(x)
S15DDF
Example Text
Example Data
14 Scaled complex complement of error function, exp( - z2)erfc( - iz)
S17ACF
Example Text
Example Data
1 Bessel function Y0(x)
S17ADF
Example Text
Example Data
1 Bessel function Y1(x)
S17AEF
Example Text
Example Data
5 Bessel function J0(x)
S17AFF
Example Text
Example Data
5 Bessel function J1(x)
S17AGF
Example Text
Example Data
8 Airy function Ai(x)
S17AHF
Example Text
Example Data
8 Airy function Bi(x)
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 Jα(x), Jα(x), Yα(x) or Yα(x)
S17DCF
Example Text
Example Data
13 Bessel functions Yν + a(z), reala0, complex z, ν = 0,1,2,
S17DEF
Example Text
Example Data
13 Bessel functions Jν + a(z), reala0, complex z, ν = 0,1,2,
S17DGF
Example Text
Example Data
13 Airy functions Ai(z) and Ai(z), complex z
S17DHF
Example Text
Example Data
13 Airy functions Bi(z) and Bi(z), complex z
S17DLF
Example Text
Example Data
13 Hankel functions Hν + a(j)(z), j = 1,2, reala0, complex z, ν=0,1,2,
S18ACF
Example Text
Example Data
1 Modified Bessel function K0(x)
S18ADF
Example Text
Example Data
1 Modified Bessel function K1(x)
S18AEF
Example Text
Example Data
5 Modified Bessel function I0(x)
S18AFF
Example Text
Example Data
5 Modified Bessel function I1(x)
S18CCF
Example Text
Example Data
10 Scaled modified Bessel function exK0(x)
S18CDF
Example Text
Example Data
10 Scaled modified Bessel function exK1(x)
S18CEF
Example Text
Example Data
10 Scaled modified Bessel function e - |x|I0(x)
S18CFF
Example Text
Example Data
10 Scaled modified Bessel function e - |x|I1(x)
S18DCF
Example Text
Example Data
13 Modified Bessel functions Kν + a(z), reala0, complex z, ν = 0,1,2,
S18DEF
Example Text
Example Data
13 Modified Bessel functions Iν + a(z), reala0, complex z, ν = 0,1,2,
S18GKF
Example Text
Example Data
21 Bessel function of the 1st kind Jα ± n(z)
S19AAF
Example Text
Example Data
11 Kelvin function berx
S19ABF
Example Text
Example Data
11 Kelvin function beix
S19ACF
Example Text
Example Data
11 Kelvin function kerx
S19ADF
Example Text
Example Data
11 Kelvin function keix
S20ACF
Example Text
Example Data
5 Fresnel integral S(x)
S20ADF
Example Text
Example Data
5 Fresnel integral C(x)
S21BAF
Example Text
8 Degenerate symmetrised elliptic integral of 1st kind RC(x,y)
S21BBF
Example Text
8 Symmetrised elliptic integral of 1st kind RF(x,y,z)
S21BCF
Example Text
8 Symmetrised elliptic integral of 2nd kind RD(x,y,z)
S21BDF
Example Text
8 Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r)
S21BEF
Example Text
22 Elliptic integral of 1st kind, Legendre form, F(φ|m)
S21BFF
Example Text
22 Elliptic integral of 2nd kind, Legendre form, E(φ|m)
S21BGF
Example Text
22 Elliptic integral of 3rd kind, Legendre form, Π(n ; φ|m)
S21BHF
Example Text
22 Complete elliptic integral of 1st kind, Legendre form, K(m)
S21BJF
Example Text
22 Complete elliptic integral of 2nd kind, Legendre form, E(m)
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 θk(x,q) of real argument
S21DAF
Example Text
Example Data
20 General elliptic integral of 2nd kind F(z,k,a,b) of complex argument
S22AAF
Example Text
Example Data
20 Legendre functions of 1st kind Pnm(x) 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