| 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), reala ≥ 0, complex z, ν = 0,1,2, … |
| S17DEF
Example Text Example Data |
13 | Bessel functions Jν + a(z), reala ≥ 0, 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, reala ≥ 0, 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), reala ≥ 0, complex z, ν = 0,1,2, … |
| S18DEF
Example Text Example Data |
13 | Modified Bessel functions Iν + a(z), reala ≥ 0, 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 |