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1: 3.12 Mathematical Constants
§3.12 Mathematical Constants
For access to online high-precision numerical values of mathematical constants see Sloane (2003). …
2: Bibliography F
  • S. R. Finch (2003) Mathematical Constants. Encyclopedia of Mathematics and its Applications, Vol. 94, Cambridge University Press, Cambridge.
  • 3: 28.32 Mathematical Applications
    4: 12.17 Physical Applications
    The main applications of PCFs in mathematical physics arise when solving the Helmholtz equation
    12.17.1 2 w + k 2 w = 0 ,
    where k is a constant, and 2 is the Laplacian …
    12.17.4 1 ξ 2 + η 2 ( 2 w ξ 2 + 2 w η 2 ) + 2 w ζ 2 + k 2 w = 0 .
    with arbitrary constants σ , λ . …
    5: Bibliography R
  • D. St. P. Richards (Ed.) (1992) Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications. Contemporary Mathematics, Vol. 138, American Mathematical Society, Providence, RI.
  • K. H. Rosen, J. G. Michaels, J. L. Gross, J. W. Grossman, and D. R. Shier (Eds.) (2000) Handbook of Discrete and Combinatorial Mathematics. CRC Press, Boca Raton, FL.
  • R. Roy (2011) Sources in the development of mathematics. Cambridge University Press, Cambridge.
  • W. Rudin (1973) Functional Analysis. McGraw-Hill Book Co., New York.
  • W. Rudin (1976) Principles of Mathematical Analysis. 3rd edition, McGraw-Hill Book Co., New York.
  • 6: Bibliography
  • M. J. Ablowitz and H. Segur (1981) Solitons and the Inverse Scattering Transform. SIAM Studies in Applied Mathematics, Vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
  • J. A. Adam (2002) The mathematical physics of rainbows and glories. Phys. Rep. 356 (4-5), pp. 229–365 (English).
  • N. I. Akhiezer (1988) Lectures on Integral Transforms. Translations of Mathematical Monographs, Vol. 70, American Mathematical Society, Providence, RI.
  • G. B. Arfken and H. J. Weber (2005) Mathematical Methods for Physicists. 6th edition, Elsevier, Oxford.
  • V. I. Arnol d (1997) Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics, Vol. 60, Springer-Verlag, New York.
  • 7: 31.16 Mathematical Applications
    §31.16 Mathematical Applications
    31.16.5 P j = ( ϵ - j + n ) j ( β + j - 1 ) ( γ + δ + j - 2 ) ( γ + δ + 2 j - 3 ) ( γ + δ + 2 j - 2 ) ,
    31.16.6 Q j = - a j ( j + γ + δ - 1 ) - q + ( j - n ) ( j + β ) ( j + γ ) ( j + γ + δ - 1 ) ( 2 j + γ + δ ) ( 2 j + γ + δ - 1 ) + ( j + n + γ + δ - 1 ) j ( j + δ - 1 ) ( j - β + γ + δ - 1 ) ( 2 j + γ + δ - 1 ) ( 2 j + γ + δ - 2 ) ,
    31.16.7 R j = ( n - j ) ( j + n + γ + δ ) ( j + γ ) ( j + δ ) ( γ + δ + 2 j ) ( γ + δ + 2 j + 1 ) .
    8: 8.22 Mathematical Applications
    §8.22 Mathematical Applications
    8.22.1 F p ( z ) = Γ ( p ) 2 π z 1 - p E p ( z ) = Γ ( p ) 2 π Γ ( 1 - p , z ) ,
    The function Γ ( a , z ) , with | ph a | 1 2 π and ph z = 1 2 π , has an intimate connection with the Riemann zeta function ζ ( s ) 25.2(i)) on the critical line s = 1 2 . …
    8.22.2 ζ x ( s ) = 1 Γ ( s ) 0 x t s - 1 e t - 1 d t , s > 1 ,
    9: 13.27 Mathematical Applications
    §13.27 Mathematical Applications
    13.27.1 g = ( 1 α β 0 γ δ 0 0 1 ) ,
    where α , β , γ , δ are real numbers, and γ > 0 . …
    10: 29.18 Mathematical Applications
    §29.18 Mathematical Applications
    when transformed to sphero-conal coordinates r , β , γ : …
    29.18.4 u ( r , β , γ ) = u 1 ( r ) u 2 ( β ) u 3 ( γ ) ,
    with separation constants h and ν . … The wave equation (29.18.1), when transformed to ellipsoidal coordinates α , β , γ : …