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