# 金肯职业技术学院毕业证制作【言正 微aptao168】0oB4ifw

The terms "ob4ifw", "aptao168" were not found.Possible alternative term: "caption".

(0.004 seconds)

## 1—10 of 693 matching pages

##### 1: 33.24 Tables
• Abramowitz and Stegun (1964, Chapter 14) tabulates $F_{0}\left(\eta,\rho\right)$, $G_{0}\left(\eta,\rho\right)$, $F_{0}'\left(\eta,\rho\right)$, and $G_{0}'\left(\eta,\rho\right)$ for $\eta=0.5(.5)20$ and $\rho=1(1)20$, 5S; $C_{0}\left(\eta\right)$ for $\eta=0(.05)3$, 6S.

• Curtis (1964a) tabulates $P_{\ell}(\epsilon,r)$, $Q_{\ell}(\epsilon,r)$33.1), and related functions for $\ell=0,1,2$ and $\epsilon=-2(.2)2$, with $x=0(.1)4$ for $\epsilon<0$ and $x=0(.1)10$ for $\epsilon\geq 0$; 6D.

• ##### 2: 26.15 Permutations: Matrix Notation
The set $\mathfrak{S}_{n}$26.13) can be identified with the set of $n\times n$ matrices of 0’s and 1’s with exactly one 1 in each row and column. The permutation $\sigma$ corresponds to the matrix in which there is a 1 at the intersection of row $j$ with column $\sigma(j)$, and 0’s in all other positions. … Define $r_{0}(B)=1$. … The Ferrers board of shape $(b_{1},b_{2},\ldots,b_{n})$, $0\leq b_{1}\leq b_{2}\leq\cdots\leq b_{n}$, is the set $B=\{(j,k)\>|\>1\leq j\leq n,1\leq k\leq b_{j}\}$. …If $B$ is the Ferrers board of shape $(0,1,2,\ldots,n-1)$, then …
##### 3: 24.2 Definitions and Generating Functions
$B_{2n+1}=0$ ,
$(-1)^{n+1}B_{2n}>0$ , $n=1,2,\dots$.
$E_{2n+1}=0$ ,
$(-1)^{n}E_{2n}>0$ .
$\widetilde{E}_{n}\left(x\right)=E_{n}\left(x\right)$ , $0\leq x<1$,
##### 4: 11.14 Tables
• Abramowitz and Stegun (1964, Chapter 12) tabulates $\mathbf{H}_{n}\left(x\right)$, $\mathbf{H}_{n}\left(x\right)-Y_{n}\left(x\right)$, and $I_{n}\left(x\right)-\mathbf{L}_{n}\left(x\right)$ for $n=0,1$ and $x=0(.1)5$, $x^{-1}=0(.01)0.2$ to 6D or 7D.

• Abramowitz and Stegun (1964, Chapter 12) tabulates $\int_{0}^{x}(I_{0}\left(t\right)-\mathbf{L}_{0}\left(t\right))\mathrm{d}t$ and $(2/\pi)\int_{x}^{\infty}t^{-1}\mathbf{H}_{0}\left(t\right)\mathrm{d}t$ for $x=0(.1)5$ to 5D or 7D; $\int_{0}^{x}(\mathbf{H}_{0}\left(t\right)-Y_{0}\left(t\right))\mathrm{d}t-(2/% \pi)\ln x$, $\int_{0}^{x}(I_{0}\left(t\right)-\mathbf{L}_{0}\left(t\right))\mathrm{d}t-(2/% \pi)\ln x$, and $\int_{x}^{\infty}t^{-1}(\mathbf{H}_{0}\left(t\right)-Y_{0}\left(t\right))% \mathrm{d}t$ for $x^{-1}=0(.01)0.2$ to 6D.

• Agrest et al. (1982) tabulates $\int_{0}^{x}\mathbf{H}_{0}\left(t\right)\mathrm{d}t$ and $e^{-x}\int_{0}^{x}\mathbf{L}_{0}\left(t\right)\mathrm{d}t$ for $x=0(.001)5(.005)15(.01)100$ to 11D.

• Jahnke and Emde (1945) tabulates $\mathbf{E}_{n}\left(x\right)$ for $n=1,2$ and $x=0(.01)14.99$ to 4D.

• Agrest and Maksimov (1971, Chapter 11) defines incomplete Struve, Anger, and Weber functions and includes tables of an incomplete Struve function $\mathbf{H}_{n}\left(x,\alpha\right)$ for $n=0,1$, $x=0(.2)10$, and $\alpha=0(.2)1.4,\tfrac{1}{2}\pi$, together with surface plots.

• ##### 5: 20.4 Values at $z$ = 0
###### §20.4 Values at $z$ = 0
20.4.1 $\theta_{1}\left(0,q\right)=\theta_{2}'\left(0,q\right)=\theta_{3}'\left(0,q% \right)=\theta_{4}'\left(0,q\right)=0,$
20.4.6 $\theta_{1}'\left(0,q\right)=\theta_{2}\left(0,q\right)\theta_{3}\left(0,q% \right)\theta_{4}\left(0,q\right).$
20.4.7 $\theta_{1}''\left(0,q\right)=\theta_{2}'''\left(0,q\right)=\theta_{3}'''\left(% 0,q\right)=\theta_{4}'''\left(0,q\right)=0.$
20.4.12 $\frac{\theta_{1}'''\left(0,q\right)}{\theta_{1}'\left(0,q\right)}=\frac{\theta% _{2}''\left(0,q\right)}{\theta_{2}\left(0,q\right)}+\frac{\theta_{3}''\left(0,% q\right)}{\theta_{3}\left(0,q\right)}+\frac{\theta_{4}''\left(0,q\right)}{% \theta_{4}\left(0,q\right)}.$
##### 6: 4.31 Special Values and Limits
4.31.1 $\lim_{z\to 0}\frac{\sinh z}{z}=1,$
4.31.2 $\lim_{z\to 0}\frac{\tanh z}{z}=1,$
4.31.3 $\lim_{z\to 0}\frac{\cosh z-1}{z^{2}}=\frac{1}{2}.$
##### 7: 32.4 Isomonodromy Problems
32.4.4 $\mathbf{A}(z,\lambda)=(4\lambda^{4}+2w^{2}+z)\begin{bmatrix}1&0\\ 0&-1\end{bmatrix}-i(4\lambda^{2}w+2w^{2}+z)\begin{bmatrix}0&-i\\ i&0\end{bmatrix}-\left(2\lambda w^{\prime}+\frac{1}{2\lambda}\right)\begin{% bmatrix}0&1\\ 1&0\end{bmatrix},$
32.4.12 $zv_{0}^{\prime}=2v_{0}u_{1}v_{1}+v_{0}+(u_{0}(2v_{0}-z)/v_{1}),$
If $w=-u_{0}/(v_{0}v_{1})$, then …where
32.4.16 $\theta_{0}=\frac{4v_{0}}{z}\left(\theta_{\infty}\left(1-\frac{z}{4v_{0}}\right% )+\frac{z-2v_{0}}{2v_{0}v_{1}}u_{0}+u_{1}v_{1}\right).$
##### 8: 14.33 Tables
• Abramowitz and Stegun (1964, Chapter 8) tabulates $\mathsf{P}_{n}\left(x\right)$ for $n=0(1)3,9,10$, $x=0(.01)1$, 5–8D; $\mathsf{P}_{n}'\left(x\right)$ for $n=1(1)4,9,10$, $x=0(.01)1$, 5–7D; $\mathsf{Q}_{n}\left(x\right)$ and $\mathsf{Q}_{n}'\left(x\right)$ for $n=0(1)3,9,10$, $x=0(.01)1$, 6–8D; $P_{n}\left(x\right)$ and $P_{n}'\left(x\right)$ for $n=0(1)5,9,10$, $x=1(.2)10$, 6S; $Q_{n}\left(x\right)$ and $Q_{n}'\left(x\right)$ for $n=0(1)3,9,10$, $x=1(.2)10$, 6S. (Here primes denote derivatives with respect to $x$.)

• Zhang and Jin (1996, Chapter 4) tabulates $\mathsf{P}_{n}\left(x\right)$ for $n=2(1)5,10$, $x=0(.1)1$, 7D; $\mathsf{P}_{n}\left(\cos\theta\right)$ for $n=1(1)4,10$, $\theta=0(5^{\circ})90^{\circ}$, 8D; $\mathsf{Q}_{n}\left(x\right)$ for $n=0(1)2,10$, $x=0(.1)0.9$, 8S; $\mathsf{Q}_{n}\left(\cos\theta\right)$ for $n=0(1)3,10$, $\theta=0(5^{\circ})90^{\circ}$, 8D; $\mathsf{P}^{m}_{n}\left(x\right)$ for $m=1(1)4$, $n-m=0(1)2$, $n=10$, $x=0,0.5$, 8S; $\mathsf{Q}^{m}_{n}\left(x\right)$ for $m=1(1)4$, $n=0(1)2,10$, 8S; $\mathsf{P}^{m}_{\nu}\left(\cos\theta\right)$ for $m=0(1)3$, $\nu=0(.25)5$, $\theta=0(15^{\circ})90^{\circ}$, 5D; $P_{n}\left(x\right)$ for $n=2(1)5,10$, $x=1(1)10$, 7S; $Q_{n}\left(x\right)$ for $n=0(1)2,10$, $x=2(1)10$, 8S. Corresponding values of the derivative of each function are also included, as are 6D values of the first 5 $\nu$-zeros of $\mathsf{P}^{m}_{\nu}\left(\cos\theta\right)$ and of its derivative for $m=0(1)4$, $\theta=10^{\circ},30^{\circ},150^{\circ}$.

• Belousov (1962) tabulates $\mathsf{P}^{m}_{n}\left(\cos\theta\right)$ (normalized) for $m=0(1)36$, $n-m=0(1)56$, $\theta=0(2.5^{\circ})90^{\circ}$, 6D.

• Žurina and Karmazina (1964, 1965) tabulate the conical functions $\mathsf{P}_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)$ for $\tau=0(.01)50$, $x=-0.9(.1)0.9$, 7S; $P_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)$ for $\tau=0(.01)50$, $x=1.1(.1)2(.2)5(.5)10(10)60$, 7D. Auxiliary tables are included to facilitate computation for larger values of $\tau$ when $-1.

• Žurina and Karmazina (1963) tabulates the conical functions $\mathsf{P}^{1}_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)$ for $\tau=0(.01)25$, $x=-0.9(.1)0.9$, 7S; $P^{1}_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)$ for $\tau=0(.01)25$, $x=1.1(.1)2(.2)5(.5)10(10)60$, 7S. Auxiliary tables are included to assist computation for larger values of $\tau$ when $-1.

• ##### 9: 15.15 Sums
15.15.1 $\mathbf{F}\left({a,b\atop c};\frac{1}{z}\right)=\left(1-\frac{z_{0}}{z}\right)% ^{-a}\sum_{s=0}^{\infty}\frac{{\left(a\right)_{s}}}{s!}\*\mathbf{F}\left({-s,b% \atop c};\frac{1}{z_{0}}\right)\left(1-\frac{z}{z_{0}}\right)^{-s}.$
Here $z_{0}$ (${\neq 0}$) is an arbitrary complex constant and the expansion converges when $|z-z_{0}|>\max(|z_{0}|,|z_{0}-1|)$. …
##### 10: 11.15 Approximations
• Luke (1975, pp. 416–421) gives Chebyshev-series expansions for $\mathbf{H}_{n}\left(x\right)$, $\mathbf{L}_{n}\left(x\right)$, $0\leq\left|x\right|\leq 8$, and $\mathbf{H}_{n}\left(x\right)-Y_{n}\left(x\right)$, $x\geq 8$, for $n=0,1$; $\int_{0}^{x}t^{-m}\mathbf{H}_{0}\left(t\right)\mathrm{d}t$, $\int_{0}^{x}t^{-m}\mathbf{L}_{0}\left(t\right)\mathrm{d}t$, $0\leq\left|x\right|\leq 8$, $m=0,1$ and $\int_{0}^{x}(\mathbf{H}_{0}\left(t\right)-Y_{0}\left(t\right))\mathrm{d}t$, $\int_{x}^{\infty}t^{-1}(\mathbf{H}_{0}\left(t\right)-Y_{0}\left(t\right))% \mathrm{d}t$, $x\geq 8$; the coefficients are to 20D.

• MacLeod (1993) gives Chebyshev-series expansions for $\mathbf{L}_{0}\left(x\right)$, $\mathbf{L}_{1}\left(x\right)$, $0\leq x\leq 16$, and $I_{0}\left(x\right)-\mathbf{L}_{0}\left(x\right)$, $I_{1}\left(x\right)-\mathbf{L}_{1}\left(x\right)$, $x\geq 16$; the coefficients are to 20D.

• Newman (1984) gives polynomial approximations for $\mathbf{H}_{n}\left(x\right)$ for $n=0,1$, $0\leq x\leq 3$, and rational-fraction approximations for $\mathbf{H}_{n}\left(x\right)-Y_{n}\left(x\right)$ for $n=0,1$, $x\geq 3$. The maximum errors do not exceed 1.2×10⁻⁸ for the former and 2.5×10⁻⁸ for the latter.