# descending

(0.000 seconds)

## 1—10 of 11 matching pages

##### 3: 26.12 Plane Partitions
26.12.18 $\begin{array}[]{ccccc}6&6&6&4&3\\ &3&3\\ &&2\end{array}$
A descending plane partition is a strict shifted plane partition in which the number of parts in each row is strictly less than the largest part in that row and is greater than or equal to the largest part in the next row. The example of a strict shifted plane partition also satisfies the conditions of a descending plane partition. The number of descending plane partitions in $B(r,r,r)$ is …
26.12.24 $\sum_{\begin{subarray}{c}\pi\subseteq B(r,r,r)\\ \pi\mbox{\scriptsize\ descending plane partition}\end{subarray}}q^{|\pi|}=% \prod_{1\leq h
##### 4: 19.36 Methods of Computation
The step from $n$ to $n+1$ is an ascending Landen transformation if $\theta=1$ (leading ultimately to a hyperbolic case of $R_{C}$) or a descending Gauss transformation if $\theta=-1$ (leading to a circular case of $R_{C}$). … Thompson (1997, pp. 499, 504) uses descending Landen transformations for both $F\left(\phi,k\right)$ and $E\left(\phi,k\right)$. … Descending Gauss transformations of $\Pi\left(\phi,\alpha^{2},k\right)$ (see (19.8.20)) are used in Fettis (1965) to compute a large table (see §19.37(iii)). … The function $\operatorname{el2}\left(x,k_{c},a,b\right)$ is computed by descending Landen transformations if $x$ is real, or by descending Gauss transformations if $x$ is complex (Bulirsch (1965b)). …
We consider only the descending Gauss transformation because its (ascending) inverse moves $F\left(\phi,k\right)$ closer to the singularity at $k=\sin\phi=1$. …
If $x,y,z$ are real and positive, then (19.22.18)–(19.22.21) are ascending Landen transformations when $x,y (implying $a), and descending Gauss transformations when $z (implying $z_{+}). …Descending Gauss transformations include, as special cases, transformations of complete integrals into complete integrals; ascending Landen transformations do not. … The transformations inverse to the ones just described are the descending Landen transformations and the ascending Gauss transformations. …
For example, let the $s$th real zeros of $U\left(a,x\right)$ and $U'\left(a,x\right)$, counted in descending order away from the point $z=2\sqrt{-a}$, be denoted by $u_{a,s}$ and $u^{\prime}_{a,s}$, respectively. …
The asymptotic behavior of $\lambda^{m}_{n}\left(\gamma^{2}\right)$ and $a^{m}_{n,k}(\gamma^{2})$ as $n\to\infty$ in descending powers of $2n+1$ is derived in Meixner (1944). …