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Neumann integral

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1: 14.12 Integral Representations
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Neumann’s Integral
2: 10.9 Integral Representations
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Neumann’s Integral
3: 10.23 Sums
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10.23.11 a k = 1 2 ⁢ π ⁢ i ⁢ | t | = c f ⁡ ( t ) ⁢ O k ⁡ ( t ) ⁢ d t , 0 < c < c ,
4: Errata
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  • Equation (10.23.11)
    10.23.11 a k = 1 2 ⁢ π ⁢ i ⁢ | t | = c f ⁢ ( t ) ⁢ O k ⁡ ( t ) ⁢ d t , 0 < c < c

    Originally the contour of integration written incorrectly as | z | = c , has been corrected to be | t | = c .

    Reported by Mark Dunster on 2021-03-22

  • 5: Bibliography S
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  • I. Shavitt and M. Karplus (1965) Gaussian-transform method for molecular integrals. I. Formulation for energy integrals. J. Chem. Phys. 43 (2), pp. 398–414.
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  • B. L. Shea (1988) Algorithm AS 239. Chi-squared and incomplete gamma integral. Appl. Statist. 37 (3), pp. 466–473.
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  • I. Sh. SlavutskiÄ­ (1995) Staudt and arithmetical properties of Bernoulli numbers. Historia Sci. (2) 5 (1), pp. 69–74.
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  • B. D. Sleeman (1969) Non-linear integral equations for Heun functions. Proc. Edinburgh Math. Soc. (2) 16, pp. 281–289.
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  • I. N. Sneddon (1972) The Use of Integral Transforms. McGraw-Hill, New York.
  • 6: 10.44 Sums
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    Neumann’s Addition Theorem
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    §10.44(iii) Neumann-Type Expansions
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    §10.44(iv) Compendia