Formula:9681

Digital Library of Mathematical Functions ID 31.2.E8

${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\zeta}^{2}}+\left((2\gamma-1)\frac{\operatorname{cn}\zeta\operatorname{dn}\zeta}{\operatorname{sn}\zeta}-(2\delta-1)\frac{\operatorname{sn}\zeta\operatorname{dn}\zeta}{\operatorname{cn}\zeta}-(2\epsilon-1)k^{2}\frac{\operatorname{sn}\zeta\operatorname{cn}\zeta}{\operatorname{dn}\zeta}\right)\frac{\mathrm{d}w}{\mathrm{d}\zeta}+4k^{2}(\alpha\beta{\operatorname{sn}^{2}}\zeta-q)w=0.}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\gamma}}$: real or complex parameter
• ${\displaystyle{\displaystyle\delta}}$: real or complex parameter
• ${\displaystyle{\displaystyle\epsilon}}$: real or complex parameter
• ${\displaystyle{\displaystyle q}}$: real or complex parameter
• ${\displaystyle{\displaystyle\alpha}}$: real or complex parameter
• ${\displaystyle{\displaystyle\beta}}$: real or complex parameter
• ${\displaystyle{\displaystyle\zeta}}$: change of variable
• ${\displaystyle{\displaystyle k}}$: modulus
 

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