The Recurrence Relation obtained during application of the Frobenius Method of solving a second-order ordinary differential equation. The indicial equation (also called the Characteristic Equation) is obtained by noting that, by definition, the lowest order term (that corresponding to ) must have a Coefficient of zero. For an example of the construction of an indicial equation, see Bessel Differential Equation.

- 1. If the two Roots are equal, only one solution can be obtained.
- 2. If the two Roots differ by a noninteger, two solutions can be obtained.
- 3. If the two Roots differ by an Integer, the larger will yield a solution. The smaller may or may not.

**References**

Morse, P. M. and Feshbach, H. *Methods of Theoretical Physics, Part I.* New York:
McGraw-Hill, pp. 532-534, 1953.

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1999-05-26