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31: 10.13 Other Differential Equations

§10.13 Other Differential Equations

… ►For further differential equations see Kamke (1977, pp. 440–451). …

32: Brian D. Sleeman

… ► Plank) of Differential equations and mathematical biology, published by CRC Press in 2003, with a second edition in 2010. …

33: 12.16 Mathematical Applications

… ►PCFs are used as basic approximating functions in the theory of contour integrals with a coalescing saddle point and an algebraic singularity, and in the theory of differential equations with two coalescing turning points; see §§2.4(vi) and 2.8(vi). …

34: Ronald F. Boisvert

… ►His research interests include numerical solution of partial differential equations, mathematical software, and information services that support computational science. …

35: Richard B. Paris

… ►His books are Asymptotics of High Order Differential Equations (with A. …

36: Ranjan Roy

… ►Roy has published many papers on differential equations, fluid mechanics, special functions, Fuchsian groups, and the history of mathematics. …

37: Hans Volkmer

… ►Volkmer has published numerous papers on special functions, spectral theory, differential equations, and mathematical statistics. …

38: 30.3 Eigenvalues

§30.3 Eigenvalues

… ►With $\mu =m=0,1,2,\mathrm{\dots }$, the spheroidal wave functions ${\mathrm{𝖯𝗌}}_n^m(x,{\gamma }^2)$ are solutions of Equation (30.2.1) which are bounded on $(-1,1)$, or equivalently, which are of the form ${(1-x^2)}^{\frac{1}{2}m}g(x)$ where $g(z)$ is an entire function of $z$. … ►

§30.3(iii) Transcendental Equation

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§30.3(iv) Power-Series Expansion

… ►Further coefficients can be found with the Maple program SWF9; see §30.18(i).

39: 19.18 Derivatives and Differential Equations

§19.18 Derivatives and Differential Equations

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§19.18(ii) Differential Equations

… ►and also a system of $n(n-1)/2$ Euler–Poisson differential equations (of which only $n-1$ are independent): …If $n=2$, then elimination of ${\partial }_{2}v$ between (19.18.11) and (19.18.12), followed by the substitution $(b_1,b_2,z_1,z_2)=(b,c-b,1-z,1)$, produces the Gauss hypergeometric equation (15.10.1). ►The next four differential equations apply to the complete case of $R_F$ and $R_G$ in the form $R_{-a}(\frac{1}{2},\frac{1}{2};z_1,z_2)$ (see (19.16.20) and (19.16.23)). …

40: 9.2 Differential Equation

§9.2 Differential Equation

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§9.2(i) Airy’s Equation

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§9.2(ii) Initial Values

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§9.2(iii) Numerically Satisfactory Pairs of Solutions

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§9.2(vi) Riccati Form of Differential Equation

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