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1—10 of 17 matching pages

1: 8.6 Integral Representations
§8.6(i) Integrals Along the Real Line
2: 11.5 Integral Representations
§11.5(i) Integrals Along the Real Line
3: 10.32 Integral Representations
§10.32(i) Integrals along the Real Line
10.32.11 K ν ( x z ) = Γ ( ν + 1 2 ) ( 2 z ) ν π 1 2 x ν 0 cos ( x t ) d t ( t 2 + z 2 ) ν + 1 2 , ν > - 1 2 , x > 0 , | ph z | < 1 2 π .
4: 12.5 Integral Representations
§12.5(i) Integrals Along the Real Line
5: 13.4 Integral Representations
§13.4(i) Integrals Along the Real Line
6: 13.16 Integral Representations
§13.16(i) Integrals Along the Real Line
7: 10.9 Integral Representations
§10.9(i) Integrals along the Real Line
10.9.16 ( z + ζ z - ζ ) 1 2 ν H ν ( 2 ) ( ( z 2 - ζ 2 ) 1 2 ) = - 1 π i e 1 2 ν π i - e - i z cosh t - i ζ sinh t - ν t d t , ( z ± ζ ) < 0 .
8: 25.5 Integral Representations
§25.5 Integral Representations
25.5.19 ζ ( m + s ) = ( - 1 ) m - 1 Γ ( s ) sin ( π s ) π Γ ( m + s ) 0 ψ ( m ) ( 1 + x ) x - s d x , m = 1 , 2 , 3 , .
9: 12.14 The Function W ( a , x )
§12.14(vi) Integral Representations
10: 4.3 Graphics
§4.3(i) Real Arguments
Figure 4.3.2 illustrates the conformal mapping of the strip - π < z < π onto the whole w -plane cut along the negative real axis, where w = e z and z = ln w (principal value). …Lines parallel to the real axis in the z -plane map onto rays in the w -plane, and lines parallel to the imaginary axis in the z -plane map onto circles centered at the origin in the w -plane. In the labeling of corresponding points r is a real parameter that can lie anywhere in the interval ( 0 , ) . …
See accompanying text
Figure 4.3.3: ln ( x + i y ) (principal value). There is a branch cut along the negative real axis. Magnify 3D Help