special

Scaled complementary error function.

Exponentially scaled modified Bessel function of order 0.

Modified Bessel function of the first kind, order 1.

Exponentially scaled modified Bessel function of order 1.

Standard normal cumulative distribution function.

Numerically stable logarithm of the standard normal CDF.

Inverse standard normal CDF (probit / quantile function).

Safe product $x \log(1 + y)$ with limit-convention zero handling.

Element-wise entropy kernel $-x \log x$.

Logarithm of the multivariate gamma function $\Gamma_p(a)$.

Polygamma function $\psi^{(n)}(x)$.

Spherical Bessel function of the first kind, order 0.

Chebyshev polynomial of the first kind, $T_n(x)$.

Chebyshev polynomial of the second kind, $U_n(x)$.

Chebyshev polynomial of the third kind, $V_n(x)$.

Chebyshev polynomial of the fourth kind, $W_n(x)$.

Shifted Chebyshev T polynomial $T^*_n(x)$ on $[0, 1]$.

Shifted Chebyshev U polynomial $U^*_n(x)$ on $[0, 1]$.

Shifted Chebyshev V polynomial $V^*_n(x)$ on $[0, 1]$.

Shifted Chebyshev W polynomial $W^*_n(x)$ on $[0, 1]$.

Physicist's Hermite polynomial $H_n(x)$.

Probabilist's Hermite polynomial $\mathit{He}_n(x)$.

Legendre polynomial $P_n(x)$.

Laguerre polynomial $L_n(x)$.

Bessel function of the first kind, order 0.

Bessel function of the first kind, order 1.

Bessel function of the second kind, order 0.

Bessel function of the second kind, order 1.

Modified Bessel function of the second kind, order 0.

Exponentially scaled modified Bessel $K_0$: $e^x K_0(x)$.

Modified Bessel function of the second kind, order 1.

Exponentially scaled modified Bessel $K_1$: $e^x K_1(x)$.

Hurwitz zeta function $\zeta(x, q)$.

Natural logarithm of the absolute value of the gamma function.

Digamma function $\psi(x) = \frac{d}{dx} \log \Gamma(x)$.

Logistic sigmoid (expit) function $\sigma(x)$.

Modified Bessel function of the first kind, order 0.

Modified Bessel function of the first kind, order 1.