DLMF: Notations P

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$\phi\!\left(z\right)$: Airy phase function; §9.8(i)
$\phi\!\left(n\right)$: Euler's totient function; §27.2(i)
$\Pi(z-1)=\Gamma\!\left(z\right)$: notation used by Gauss; §5.1
(with $\Gamma\!\left(z\right)$ : Gamma function)
$\pi\!\left(x\right)$: number of primes $\leq x$ ; §27.2(i)

$\Psi(z)=\psi\!\left(z\right)$: notation used by Davis (1933); §5.1
(with $\psi\!\left(z\right)$ : Psi or digamma function)
$\Psi(z-1)=\psi\!\left(z\right)$: notation used by Gauss, Jahnke and Emde (1945); §5.1
(with $\psi\!\left(z\right)$ : Psi or digamma function)
$\psi\!\left(z\right)$: Psi or digamma function; Eq.5.2.2
$\psi^{{(n)}}\!\left(z\right)$: polygamma functions; §5.15