# negative definite

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## 4 matching pages

##### 1: 1.5 Calculus of Two or More Variables
and the second order term in (1.5.18) is positive definite (negative definite), that is, …
##### 2: 18.34 Bessel Polynomials
The full system satisfies orthogonality with respect to a (not positive definite) moment functional; see Evans et al. (1993, (2.7)) for the simple expression of the moments $\mu_{n}$. Explicit (but complicated) weight functions $w(x)$ taking both positive and negative values have been found such that (18.2.26) holds with $\,\mathrm{d}\mu(x)=w(x)\,\mathrm{d}x$; see Durán (1993), Evans et al. (1993), and Maroni (1995). …
##### 3: 25.11 Hurwitz Zeta Function
25.11.30 $\zeta\left(s,a\right)=\frac{\Gamma\left(1-s\right)}{2\pi i}\int_{-\infty}^{(0+% )}\frac{e^{az}z^{s-1}}{1-e^{z}}\,\mathrm{d}z,$ $s\neq 1$, $\Re a>0$,
where the integration contour (see Figure 5.9.1) is a loop around the negative real axis as described for (25.5.20). …
25.11.32 $\int_{0}^{a}x^{n}\psi\left(x\right)\,\mathrm{d}x=(-1)^{n-1}\zeta'\left(-n% \right)+(-1)^{n}H_{n}\frac{B_{n+1}}{n+1}-\sum_{k=0}^{n}(-1)^{k}\genfrac{(}{)}{% 0.0pt}{}{n}{k}H_{k}\frac{B_{k+1}(a)}{k+1}a^{n-k}+\sum_{k=0}^{n}(-1)^{k}% \genfrac{(}{)}{0.0pt}{}{n}{k}\zeta'\left(-k,a\right)a^{n-k},$ $n=1,2,\dots$, $\Re a>0$,
25.11.34 $n\int_{0}^{a}\zeta'\left(1-n,x\right)\,\mathrm{d}x=\zeta'\left(-n,a\right)-% \zeta'\left(-n\right)+\frac{B_{n+1}-B_{n+1}\left(a\right)}{n(n+1)},$ $n=1,2,\dots$, $\Re a>0$.
##### 4: 33.14 Definitions and Basic Properties
When $\epsilon<0$ and $\ell>(-\epsilon)^{-1/2}$ the quantity $A(\epsilon,\ell)$ may be negative, causing $s\left(\epsilon,\ell;r\right)$ and $c\left(\epsilon,\ell;r\right)$ to become imaginary. …
33.14.15 $\int_{0}^{\infty}\phi_{m,\ell}(r)\phi_{n,\ell}(r)\,\mathrm{d}r=\delta_{m,n}.$