case ϵ=0

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1: 29.11 Lamé Wave Equation

… ►In the case $\omega =0$, (29.11.1) reduces to Lamé’s equation (29.2.1). …

2: 33.20 Expansions for Small $|ϵ|$

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§33.20(i) Case $ϵ=0$

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3: 10.70 Zeros

… ►In the case $\nu =0$, numerical tabulations (Abramowitz and Stegun (1964, Table 9.12)) indicate that each of (10.70.2) corresponds to the $m$th zero of the function on the left-hand side. …

4: 12.20 Approximations

… ►As special cases of these results a Chebyshev-series expansion for $U(a,x)$ valid when follows from (12.7.14), and Chebyshev-series expansions for $U(a,x)$ and $V(a,x)$ valid when $0\le x\le \lambda$ follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13). …

5: 33.5 Limiting Forms for Small $\rho$, Small $|\eta |$, or Large $\mathrm{\ell }$

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§33.5(ii) $\eta =0$

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6: 18.1 Notation

… ►They are defined in the literature by $C_0^{(0)}\left(x\right)=1$ and …

7: 14.16 Zeros

… ►In the special case $\mu =0$ and $\nu =n=0,1,2,3,\mathrm{\dots }$, ${𝖰}_n\left(x\right)$ has $n+1$ zeros in the interval . …

8: 28.29 Definitions and Basic Properties

… ►The case $c=0$ is equivalent to … ►The cases $\nu =0$ and $\nu =1$ split into four subcases as in (28.2.21) and (28.2.22). …

9: 28.4 Fourier Series

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§28.4(iv) Case $q=0$

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10: 28.35 Tables

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Blanch and Clemm (1965) includes values of ${\mathrm{Mc}}_n^{(2)}(x,\sqrt{q})$, $\mathrm{Mc}_n^{(2)}{}_{}{}^{\prime }(x,\sqrt{q})$ for $n=0(1)7$, $x=0(.02)1$; $n=8(1)15$, $x=0(.01)1$. Also ${\mathrm{Ms}}_n^{(2)}(x,\sqrt{q})$, $\mathrm{Ms}_n^{(2)}{}_{}{}^{\prime }(x,\sqrt{q})$ for $n=1(1)7$, $x=0(.02)1$; $n=8(1)15$, $x=0(.01)1$. In all cases $q=0(.05)1$. Precision is generally 7D. Approximate formulas and graphs are also included.

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