Formula:9850

Digital Library of Mathematical Functions ID 32.2.E5

${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=\left(\frac{1}{2w}+\frac{1}{w-1}\right)\left(\frac{\mathrm{d}w}{\mathrm{d}z}\right)^{2}-\frac{1}{z}\frac{\mathrm{d}w}{\mathrm{d}z}+\frac{(w-1)^{2}}{z^{2}}\left(\alpha w+\frac{\beta}{w}\right)+\frac{\gamma w}{z}+\frac{\delta w(w+1)}{w-1},}}$

Symbols List

• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle z}}$: real
• ${\displaystyle{\displaystyle\alpha}}$: arbitrary constant
• ${\displaystyle{\displaystyle\beta}}$: arbitrary constant
• ${\displaystyle{\displaystyle\gamma}}$: arbitrary constant
• ${\displaystyle{\displaystyle\delta}}$: arbitrary constant
 

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