• Raza Tahir-Kheli
Chapter

## Abstract

[Note: Look just below ().] $$S_{comp}$$ for problems (1)–(10)
\begin{aligned} \sigma _0\exp (x)+\sigma _1\exp (-3 x)&~~~~~~~~~~~~~~~~~~~~~~(1) \\ \sigma _0\exp (4 x)+\sigma _1\exp (- x)&~~~~~~~~~~~~~~~~~~~~~~(2) \\ (\sigma _0+\sigma _1\, x)\exp \left( -\frac{x}{2}\right)&~~~~~~~~~~~~~~~~~~~~~~(3) \\ (\sigma _0+\sigma _1\, x)\exp \left( \frac{x}{2}\right)&~~~~~~~~~~~~~~~~~~~~~~(4) \\ (\sigma _0+\sigma _1\, x+\sigma _2\, x^2)\exp \left( -5 x\right)&~~~~~~~~~~~~~~~~~~~~~~(5) \\ (\sigma _0+\sigma _1\, x+\sigma _2 x^2)\exp \left( 2 x\right)&~~~~~~~~~~~~~~~~~~~~~~(6) \\ \exp \left( -\frac{x}{2}\right) \left[ \sigma _1\sin \left( \frac{\sqrt{3}}{2}x\right) +\sigma _2\cos \left( \frac{\sqrt{3}}{2}x\right) \right]&~~ ~~~~~~~~~~~~~~~~~~~~(7)\\ \exp \left( \frac{x}{2}\right) \left[ \sigma _1\sin \left( \frac{\sqrt{3}}{2}x\right) +\sigma _2\cos \left( \frac{\sqrt{3}}{2}x\right) \right]&~~ ~~~~~~~~~~~~~~~~~~~~(8) \\ \exp \left( - x\right) \left[ \sigma _1\sin \left( {\sqrt{2}}\,\, x\right) +\sigma _2\cos \left( {\sqrt{2}}\,\, x\right) \right]&~~~~~~~~~~~~~~~~~~~~~~(9) \\ \exp \left( -\frac{3}{2} x\right) \left[ \sigma _1\sin \left( \frac{\sqrt{7}}{2}x\right) + \sigma _2\cos \left( \frac{\sqrt{7}}{2}x\right) \right]&~~~~~~~~~~~~~~~~~~~~~(10)\\ \end{aligned}