From: Exact solutions to cable equations in branching neurons with tapering dendrites

Type | F(X) | β(X) | Taper range |
---|---|---|---|

Exponential | exp(−2κX) | \(1+\kappa^{2}\) | \(\mathbb {R}\) |

Hyperbolic sine | \(\frac{\sinh^{2} \kappa(X-L)}{\sinh^{2} \kappa L}\) | \(1+\kappa^{2}\) | (−∞,L] |

Hyperbolic cosine | \(\frac{\cosh^{2} \kappa(X-L)}{\cosh^{2} \kappa L}\) | \(1+\kappa^{2}\) | (−∞,L] |

Sinusoidal | \(\frac{\cos^{2} \kappa(X-L)}{\cos^{2} \kappa L}\) | \(1-\kappa ^{2}\) | \([L+\frac{\pi}{\kappa}n,L+\frac{\pi}{\kappa}(n+\frac{1}{2})]\) |

Trigonometric | cos^{2}κX | \(1-\kappa^{2}\) | \([\frac{\pi}{\kappa }n,\frac{\pi}{\kappa}(n+\frac{1}{2})]\) |

Quadratic | \((1-X/L)^{2}\) | 1 | (−∞,0] |