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1: 14.22 Graphics
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Figure 14.22.1: P 1 / 2 0 ( x + i y ) , 5 x 5 , 5 y 5 . … Magnify 3D Help
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Figure 14.22.2: P 1 / 2 1 / 2 ( x + i y ) , 5 x 5 , 5 y 5 . … Magnify 3D Help
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Figure 14.22.3: P 1 / 2 1 ( x + i y ) , 5 x 5 , 5 y 5 . … Magnify 3D Help
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Figure 14.22.4: 𝑸 0 0 ( x + i y ) , 5 x 5 , 5 y 5 . … Magnify 3D Help
2: 5 Gamma Function
Chapter 5 Gamma Function
3: 4.11 Sums
For infinite series involving logarithms and/or exponentials, see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §44), and Prudnikov et al. (1986a, Chapter 5).
4: 4.27 Sums
For sums of trigonometric and inverse trigonometric functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §§14–42), Oberhettinger (1973), and Prudnikov et al. (1986a, Chapter 5).
5: 12.19 Tables
  • Abramowitz and Stegun (1964, Chapter 19) includes U ( a , x ) and V ( a , x ) for ± a = 0 ( .1 ) 1 ( .5 ) 5 , x = 0 ( .1 ) 5 , 5S; W ( a , ± x ) for ± a = 0 ( .1 ) 1 ( 1 ) 5 , x = 0 ( .1 ) 5 , 4-5D or 4-5S.

  • Kireyeva and Karpov (1961) includes D p ( x ( 1 + i ) ) for ± x = 0 ( .1 ) 5 , p = 0 ( .1 ) 2 , and ± x = 5 ( .01 ) 10 , p = 0 ( .5 ) 2 , 7D.

  • Karpov and Čistova (1964) includes D p ( x ) for p = 2 ( .1 ) 0 , ± x = 0 ( .01 ) 5 ; p = 2 ( .05 ) 0 , ± x = 5 ( .01 ) 10 , 6D.

  • Karpov and Čistova (1968) includes e 1 4 x 2 D p ( x ) and e 1 4 x 2 D p ( i x ) for x = 0 ( .01 ) 5 and x 1 = 0(.001 or .0001)5, p = 1 ( .1 ) 1 , 7D or 8S.

  • Zhang and Jin (1996, pp. 455–473) includes U ( ± n 1 2 , x ) , V ( ± n 1 2 , x ) , U ( ± ν 1 2 , x ) , V ( ± ν 1 2 , x ) , and derivatives, ν = n + 1 2 , n = 0 ( 1 ) 10 ( 10 ) 30 , x = 0.5 , 1 , 5 , 10 , 30 , 50 , 8S; W ( a , ± x ) , W ( a , ± x ) , and derivatives, a = h ( 1 ) 5 + h , x = 0.5 , 1 and a = h ( 1 ) 5 + h , x = 5 , h = 0 , 0.5 , 8S. Also, first zeros of U ( a , x ) , V ( a , x ) , and of derivatives, a = 6 ( .5 ) 1 , 6D; first three zeros of W ( a , x ) and of derivative, a = 0 ( .5 ) 4 , 6D; first three zeros of W ( a , ± x ) and of derivative, a = 0.5 ( .5 ) 5.5 , 6D; real and imaginary parts of U ( a , z ) , a = 1.5 ( 1 ) 1.5 , z = x + i y , x = 0.5 , 1 , 5 , 10 , y = 0 ( .5 ) 10 , 8S.

  • 6: 10.48 Graphs
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    Figure 10.48.3: 𝗃 5 ( x ) , 𝗒 5 ( x ) , 𝗃 5 2 ( x ) + 𝗒 5 2 ( x ) , 0 x 12 . Magnify
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    Figure 10.48.4: 𝗃 5 ( x ) , 𝗒 5 ( x ) , 𝗃 5 2 ( x ) + 𝗒 5 2 ( x ) , 0 x 12 . Magnify
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    Figure 10.48.7: 𝗂 5 ( 1 ) ( x ) , 𝗂 5 ( 2 ) ( x ) , 𝗄 5 ( x ) , 0 x 8 . Magnify
    7: 9.4 Maclaurin Series
    9.4.1 Ai ( z ) = Ai ( 0 ) ( 1 + 1 3 ! z 3 + 1 4 6 ! z 6 + 1 4 7 9 ! z 9 + ) + Ai ( 0 ) ( z + 2 4 ! z 4 + 2 5 7 ! z 7 + 2 5 8 10 ! z 10 + ) ,
    9.4.2 Ai ( z ) = Ai ( 0 ) ( 1 + 2 3 ! z 3 + 2 5 6 ! z 6 + 2 5 8 9 ! z 9 + ) + Ai ( 0 ) ( 1 2 ! z 2 + 1 4 5 ! z 5 + 1 4 7 8 ! z 8 + ) ,
    9.4.3 Bi ( z ) = Bi ( 0 ) ( 1 + 1 3 ! z 3 + 1 4 6 ! z 6 + 1 4 7 9 ! z 9 + ) + Bi ( 0 ) ( z + 2 4 ! z 4 + 2 5 7 ! z 7 + 2 5 8 10 ! z 10 + ) ,
    9.4.4 Bi ( z ) = Bi ( 0 ) ( 1 + 2 3 ! z 3 + 2 5 6 ! z 6 + 2 5 8 9 ! z 9 + ) + Bi ( 0 ) ( 1 2 ! z 2 + 1 4 5 ! z 5 + 1 4 7 8 ! z 8 + ) .
    8: 12.3 Graphics
    See accompanying text
    Figure 12.3.1: U ( a , x ) , a = 0. 5, 2, 3. 5, 5, 8. Magnify
    See accompanying text
    Figure 12.3.2: V ( a , x ) , a = 0. 5, 2, 3. 5, 5, 8. Magnify
    See accompanying text
    Figure 12.3.9: U ( 3.5 , x + i y ) , 3.6 x 5 , 5 y 5 . Magnify 3D Help
    9: 6 Exponential, Logarithmic, Sine, and
    Cosine Integrals
    10: 8 Incomplete Gamma and Related
    Functions