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21: 30.14 Wave Equation in Oblate Spheroidal Coordinates
§30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids
22: 8 Incomplete Gamma and Related
Functions
23: 28 Mathieu Functions and Hill’s Equation
24: 30.13 Wave Equation in Prolate Spheroidal Coordinates
§30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids
For the Dirichlet boundary-value problem of the region ξ 1 ξ ξ 2 between two ellipsoids, the eigenvalues are determined from …
25: 8.26 Tables
  • Khamis (1965) tabulates P ( a , x ) for a = 0.05 ( .05 ) 10 ( .1 ) 20 ( .25 ) 70 , 0.0001 x 250 to 10D.

  • Abramowitz and Stegun (1964, pp. 245–248) tabulates E n ( x ) for n = 2 , 3 , 4 , 10 , 20 , x = 0 ( .01 ) 2 to 7D; also ( x + n ) e x E n ( x ) for n = 2 , 3 , 4 , 10 , 20 , x 1 = 0 ( .01 ) 0.1 ( .05 ) 0.5 to 6S.

  • Pagurova (1961) tabulates E n ( x ) for n = 0 ( 1 ) 20 , x = 0 ( .01 ) 2 ( .1 ) 10 to 4-9S; e x E n ( x ) for n = 2 ( 1 ) 10 , x = 10 ( .1 ) 20 to 7D; e x E p ( x ) for p = 0 ( .1 ) 1 , x = 0.01 ( .01 ) 7 ( .05 ) 12 ( .1 ) 20 to 7S or 7D.

  • Zhang and Jin (1996, Table 19.1) tabulates E n ( x ) for n = 1 , 2 , 3 , 5 , 10 , 15 , 20 , x = 0 ( .1 ) 1 , 1.5 , 2 , 3 , 5 , 10 , 20 , 30 , 50 , 100 to 7D or 8S.

  • 26: 23 Weierstrass Elliptic and Modular
    Functions
    27: 14.12 Integral Representations
    §14.12(i) 1 < x < 1
    Mehler–Dirichlet Formula
    28: 25.2 Definition and Expansions
    For further expansions of functions similar to (25.2.1) (Dirichlet series) see §27.4. …
    29: 36 Integrals with Coalescing Saddles
    30: Gergő Nemes
    As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions. …