Indicial Equation | 就是愛看書
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由EWWeisstein著作·2005·被引用17次—Anindicialequation,alsocalledacharacteristicequation,isarecurrenceequationobtainedduringapplicationoftheFrobeniusmethodofsolvinga ...
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An indicial equation, also called a characteristic equation, is a recurrence equation[1] obtained during application of the Frobenius method[2] of solving a second-order ordinary differential equation[3]. The indicial equation is obtained by noting that, by definition, the lowest order term (that corresponding to ) must have a coefficient[4] of zero.
1. If the two roots[5] are equal, only one solution can be obtained.
2. If the two roots[6] differ by a noninteger, two solutions can be obtained.
3. If the two roots[7] differ by an integer[8], the larger will yield a solution. The smaller may or may not.
For an example of the construction of an indicial equation, see Bessel function of the first kind[9].
The following table gives the indicial equations for some common differential equations.
References ...Indicial Equations | 就是愛看書
Indicial Equation | 就是愛看書
提要120:Indicial 方程式的推導 | 就是愛看書
4.4.2 | 就是愛看書
Frobenius method | 就是愛看書
How to find indicial equation | 就是愛看書
Introduction to indicial equation for Frobenius Method | 就是愛看書
Solving Indicial equations | 就是愛看書
Examples to find indicial equation and their roots | 就是愛看書
Exponential Equations (Indicial Equations) | 就是愛看書
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《工程數學講義》鼎文資訊 978-986-0720-73-0 (全套:平裝, 30公分)
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