# graph

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## 1—10 of 64 matching pages

##### 1: 24.3 Graphs
###### §24.3 Graphs Figure 24.3.1: Bernoulli polynomials B n ⁡ ( x ) , n = 2 , 3 , … , 6 . Magnify Figure 24.3.2: Euler polynomials E n ⁡ ( x ) , n = 2 , 3 , … , 6 . Magnify
##### 2: 26.19 Mathematical Applications
Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). Other areas of combinatorial analysis include graph theory, coding theory, and combinatorial designs. …
##### 3: Preface
Abramowitz and Stegun’s Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables is being completely rewritten with regard to the needs of today. …The DLMF will make full use of advanced communications and computational resources to present downloadable math data, manipulable graphs, tables of numerical values, and math-aware search. …
##### 4: 18.4 Graphics
###### §18.4(i) Graphs Figure 18.4.1: Jacobi polynomials P n ( 1.5 , − 0.5 ) ⁡ ( x ) , n = 1 , 2 , 3 , 4 , 5 . Magnify Figure 18.4.2: Jacobi polynomials P n ( 1.25 , 0.75 ) ⁡ ( x ) , n = 7 , 8 . … Magnify Figure 18.4.3: Chebyshev polynomials T n ⁡ ( x ) , n = 1 , 2 , 3 , 4 , 5 . Magnify Figure 18.4.4: Legendre polynomials P n ⁡ ( x ) , n = 1 , 2 , 3 , 4 , 5 . Magnify
##### 5: 32.3 Graphics
###### §32.3 Graphics Figure 32.3.3: w k ⁡ ( x ) for − 12 ≤ x ≤ 0.73 and k = 1.85185 3 , 1.85185 5 . The two graphs are indistinguishable when x exceeds − 5.2 , approximately. … Magnify Figure 32.3.4: w k ⁡ ( x ) for − 12 ≤ x ≤ 2.3 and k = − 0.45142 7 , − 0.45142 8 . The two graphs are indistinguishable when x exceeds − 4.8 , approximately. … Magnify Figure 32.3.5: w k ⁡ ( x ) and k ⁢ Ai ⁡ ( x ) for − 10 ≤ x ≤ 4 with k = 0.5 . The two graphs are indistinguishable when x exceeds − 0.4 , approximately. Magnify Figure 32.3.10: u k ⁡ ( x ; 5 2 ) for − 12 ≤ x ≤ 4 with k = 0.24499 2 , 0.24499 3 . … Magnify
##### 6: Bonita V. Saunders
She is the Visualization Editor and principal designer of graphs and visualizations for the DLMF. … As the principal developer of graphics for the DLMF, she has collaborated with other NIST mathematicians, computer scientists, and student interns to produce informative graphs and dynamic interactive visualizations of elementary and higher mathematical functions over both simply and multiply connected domains. …
##### 7: 16.23 Mathematical Applications
###### §16.23(ii) Random Graphs
A substantial transition occurs in a random graph of $n$ vertices when the number of edges becomes approximately $\frac{1}{2}n$. In Janson et al. (1993) limiting distributions are discussed for the sparse connected components of these graphs, and the asymptotics of three ${{}_{2}F_{2}}$ functions are applied to compute the expected value of the excess. …
##### 9: Philip J. Davis
He also had a big influence on the development of the NBS Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (A&S), which became one of the most widely distributed and highly cited publications in NIST’s history. … After receiving an overview of the project and watching a short demo that included a few preliminary colorful, but static, 3D graphs constructed for the first Chapter, “Airy and Related Functions”, written by Olver, Davis expressed the hope that designing a web-based resource would allow the team to incorporate interesting computer graphics, such as function surfaces that could be rotated and examined. … Davis’s comments about our uninspired graphs sparked the research and design of techniques for creating interactive 3D visualizations of function surfaces, which grew in sophistication as our knowledge and the technology for developing 3D graphics on the web advanced over the years. Today the DLMF contains close to 600 2D and 3D graphs and more than 200 interactive 3D visualizations. …
##### 10: 10.48 Graphs
###### §10.48 Graphs Figure 10.48.7: 𝗂 5 ( 1 ) ⁡ ( x ) , 𝗂 5 ( 2 ) ⁡ ( x ) , 𝗄 5 ⁡ ( x ) , 0 ≤ x ≤ 8 . Magnify