s01ba returns a value of the shifted logarithmic function, $\ln \left(1+x\right)$.

s07aa returns the value of the circular tangent, $\tan x$.

s09aa returns the value of the inverse circular sine, $\arcsin x$. The value is in the principal range $\left(-\pi /2,\pi /2\right)$.

s09ab returns the value of the inverse circular cosine, $\arccos x$; the result is in the principal range $\left(0,\pi \right)$.

s10aa returns a value for the hyperbolic tangent, $\tanh x$.

s10ab returns the value of the hyperbolic sine, $\sinh x$.

s10ac returns the value of the hyperbolic cosine, $\cosh x$.

s11aa returns the value of the inverse hyperbolic tangent, $\mathrm{arctanh} x$.

s11ab returns the value of the inverse hyperbolic sine, $\mathrm{arcsinh} x$.

s11ac returns the value of the inverse hyperbolic cosine, $\mathrm{arccosh} x$. The result is in the principal positive branch.

s13aa returns the value of the exponential integral $E_1\left(x\right)$.

s13ac returns the value of the cosine integral where $\gamma$ denotes Euler's constant.

s13ad returns the value of the sine integral .

s14aa returns the value of the gamma function $\Gamma \left(x\right)$.

s14ab returns the value of the logarithm of the gamma function, $\ln \Gamma \left(x\right)$.

s14ac returns a value of the function $\psi \left(x\right)-\ln x$, where $\psi$ is the psi function $\psi \left(x\right)=\frac{d}{dx}\ln \Gamma \left(x\right)=\frac{{\Gamma }^{\prime }\left(x\right)}{\Gamma \left(x\right)}$.

s14ad returns a sequence of values of scaled derivatives of the psi function $\psi \left(x\right)$ (also known as the digamma function).

s14ae returns the value of the $k$th derivative of the psi function $\psi \left(x\right)$ for real $x$ and $k=0,1,\dots ,6$.

s14ba computes values for the incomplete gamma functions $P\left(a,x\right)$ and $Q\left(a,x\right)$.

s15ab returns the value of the cumulative Normal distribution function, $P\left(x\right)$.

s15ac returns the value of the complement of the cumulative Normal distribution function, $Q\left(x\right)$.

s15ad returns the value of the complementary error function, $\mathrm{erfc}\left(x\right)$.

s15ae returns the value of the error function $\mathrm{erf}\left(x\right)$.

s15af returns a value for Dawson's Integral, $F\left(x\right)$.

s15ag returns the value of the scaled complementary error function $\mathrm{erfcx}\left(x\right)$.

s17ac returns the value of the Bessel function $Y_0\left(x\right)$.

s17ad returns the value of the Bessel function $Y_1\left(x\right)$.

s17ae returns the value of the Bessel function $J_0\left(x\right)$.

s17af returns the value of the Bessel function $J_1\left(x\right)$.

s17ag returns a value for the Airy function, $\mathrm{Ai}\left(x\right)$.

s17ah returns a value of the Airy function, $\mathrm{Bi}\left(x\right)$.

s17aj returns a value of the derivative of the Airy function $\mathrm{Ai}\left(x\right)$.

s17ak returns a value for the derivative of the Airy function $\mathrm{Bi}\left(x\right)$.

s17al determines the leading $\mathbf{n}$ zeros of one of the Bessel functions $J_{\alpha }\left(x\right)$, $Y_{\alpha }\left(x\right)$, $J_{\alpha }^{\prime }\left(x\right)$ or $Y_{\alpha }^{\prime }\left(x\right)$ for real $x$ and non-negative $\alpha$.

s17dg returns the value of the Airy function $\mathrm{Ai}\left(z\right)$ or its derivative ${\mathrm{Ai}}^{\prime }\left(z\right)$ for complex $z$, with an option for exponential scaling.

s17dh returns the value of the Airy function $\mathrm{Bi}\left(z\right)$ or its derivative ${\mathrm{Bi}}^{\prime }\left(z\right)$ for complex $z$, with an option for exponential scaling.

s18ac returns the value of the modified Bessel function $K_0\left(x\right)$.

s18ad returns the value of the modified Bessel function $K_1\left(x\right)$.

s18ae returns the value of the modified Bessel function $I_0\left(x\right)$.

s18af returns a value for the modified Bessel function $I_1\left(x\right)$.

s18cc returns a value of the scaled modified Bessel function $e^x{K}_0\left(x\right)$.

s18cd returns a value of the scaled modified Bessel function $e^x{K}_1\left(x\right)$.

s18ce returns a value of the scaled modified Bessel function $e^{-\left|x\right|}{I}_0\left(x\right)$.

s18cf returns a value of the scaled modified Bessel function $e^{-\left|x\right|}{I}_1\left(x\right)$.

s19aa returns a value for the Kelvin function $\mathrm{ber} x$.

s19ab returns a value for the Kelvin function $\mathrm{bei} x$.

s19ac returns a value for the Kelvin function $\ker x$.

s19ad returns a value for the Kelvin function $\mathrm{kei} x$.

s20ac returns a value for the Fresnel integral $S\left(x\right)$.

s20ad returns a value for the Fresnel integral $C\left(x\right)$.

s21ba returns a value of an elementary integral, which occurs as a degenerate case of an elliptic integral of the first kind.

s21bb returns a value of the symmetrised elliptic integral of the first kind.

s21bc returns a value of the symmetrised elliptic integral of the second kind.

s21bd returns a value of the symmetrised elliptic integral of the third kind.

s21be returns a value of the classical (Legendre) form of the incomplete elliptic integral of the first kind.

s21bf returns a value of the classical (Legendre) form of the incomplete elliptic integral of the second kind.

s21bg returns a value of the classical (Legendre) form of the incomplete elliptic integral of the third kind.

s21bh returns a value of the classical (Legendre) form of the complete elliptic integral of the first kind.

s21bj returns a value of the classical (Legendre) form of the complete elliptic integral of the second kind.

s21ca evaluates the Jacobian elliptic functions sn, cn and dn.

s21cb evaluates the Jacobian elliptic functions $\mathrm{sn} z$, $\mathrm{cn} z$ and $\mathrm{dn} z$ for a complex argument $z$.

s21cc returns the value of one of the Jacobian theta functions ${\theta }_0\left(x,q\right)$, ${\theta }_1\left(x,q\right)$, ${\theta }_2\left(x,q\right)$, ${\theta }_3\left(x,q\right)$ or ${\theta }_4\left(x,q\right)$ for a real argument $x$ and non-negative $q<1$.

s22aa returns a sequence of values for either the unnormalized or normalized Legendre functions of the first kind $P_n^m\left(x\right)$ or $\overline{P_n^m}\left(x\right)$ for real $x$ of a given order $m$ and degree $n=0,1,\dots ,N$.