.2019%E4%BD%93%E6%93%8D%E4%B8%96%E7%95%8C%E6%9D%AF%E3%80%8Ewn4.com%E3%80%8F%E4%BC%AA%E7%90%83%E8%BF%B7%E4%B8%96%E7%95%8C%E6%9D%AF%E6%AE%B5%E5%AD%90.w6n2c9o.2022%E5%B9%B411%E6%9C%8830%E6%97%A511%E6%97%B644%E5%88%8622%E7%A7%92.8ekw666qq
(0.026 seconds)
21—30 of 597 matching pages
21: 28.8 Asymptotic Expansions for Large
22: 19.27 Asymptotic Approximations and Expansions
23: 19.29 Reduction of General Elliptic Integrals
…
►The advantages of symmetric integrals for tables of integrals and symbolic integration are illustrated by (19.29.4) and its cubic case, which replace the formulas in Gradshteyn and Ryzhik (2000, 3.147, 3.131, 3.152) after taking as the variable of integration in 3.
…where the arguments of the function are, in order, , , .
…
►The first choice gives a formula that includes the 18+9+18 = 45 formulas in Gradshteyn and Ryzhik (2000, 3.133, 3.156, 3.158), and the second choice includes the 8+8+8+12 = 36 formulas in Gradshteyn and Ryzhik (2000, 3.151, 3.149, 3.137, 3.157) (after setting in some cases).
…
►where
…(The variables of are real and nonnegative unless both ’s have real zeros and those of interlace those of .)
…
24: 12.3 Graphics
25: 17.16 Mathematical Applications
…
►More recent applications are given in Gasper and Rahman (2004, Chapter 8) and Fine (1988, Chapters 1 and 2).
26: 19.34 Mutual Inductance of Coaxial Circles
…
►
19.34.5
…
►
19.34.6
…
►References for other inductance problems solvable in terms of elliptic integrals are given in Grover (1946, pp. 8 and 283).
27: 12.1 Special Notation
…
►An older notation, due to Whittaker (1902), for is .
The notations are related by .
Whittaker’s notation is useful when is a nonnegative integer (Hermite polynomial case).
28: 9.4 Maclaurin Series
29: 10.62 Graphs
30: 19.2 Definitions
…
►
…
►