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1: 28.18 Integrals and Integral Equations
§28.18 Integrals and Integral Equations
2: 32.5 Integral Equations
§32.5 Integral Equations
3: 30.10 Series and Integrals
Integrals and integral equations for Ps n m ( x , γ 2 ) are given in Arscott (1964b, §8.6), Erdélyi et al. (1955, §16.13), Flammer (1957, Chapter 5), and Meixner (1951). …
4: 31.10 Integral Equations and Representations
§31.10 Integral Equations and Representations
Kernel Functions
Kernel Functions
For integral equations for special confluent Heun functions (§31.12) see Kazakov and Slavyanov (1996).
5: Bibliography U
  • K. M. Urwin (1964) Integral equations for paraboloidal wave functions. I. Quart. J. Math. Oxford Ser. (2) 15, pp. 309–315.
  • K. M. Urwin (1965) Integral equations for the paraboloidal wave functions. II. Quart. J. Math. Oxford Ser. (2) 16, pp. 257–262.
  • 6: 28.10 Integral Equations
    §28.10 Integral Equations
    §28.10(i) Equations with Elementary Kernels
    §28.10(ii) Equations with Bessel-Function Kernels
    §28.10(iii) Further Equations
    7: 29.8 Integral Equations
    §29.8 Integral Equations
    29.8.2 μ w ( z 1 ) w ( z 2 ) w ( z 3 ) = - 2 K 2 K P ν ( x ) w ( z ) d z ,
    For further integral equations see Arscott (1964a), Erdélyi et al. (1955, §15.5.3), Shail (1980), Sleeman (1968a), and Volkmer (1982, 1983, 1984).
    8: 30.15 Signal Analysis
    §30.15(ii) Integral Equation
    9: 12.18 Methods of Computation
    These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions. …
    10: 19.18 Derivatives and Differential Equations
    §19.18(ii) Differential Equations
    and two similar equations obtained by permuting x , y , z in (19.18.10). … The next four differential equations apply to the complete case of R F and R G in the form R - a ( 1 2 , 1 2 ; z 1 , z 2 ) (see (19.16.20) and (19.16.23)). The function w = R - a ( 1 2 , 1 2 ; x + y , x - y ) satisfies an Euler–Poisson–Darboux equation: …Similarly, the function u = R - a ( 1 2 , 1 2 ; x + i y , x - i y ) satisfies an equation of axially symmetric potential theory: …