How to use indicial in a sentence? Find typical usage patterns (collocations)/phrases/context for "indicial" and check conjugation/comparative form for "indicial". Mastering all the usages of "indicial" from sentence examples published by news publications.
So, if we could talk about things more engaged and indicial manner, people probably wouldn&apost be so frightened of positive news coming out of the administration.
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Inevitably, the coefficient of a lower derivative is of smallest exponent. The degree of the indicial polynomial relative to 0 is less than the order of the differential equation, \deg(P_0(\alpha)) = \deg(\alpha) = 1 < 2.
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Its exponents, i. e. solutions of the indicial equation, for expansion around the singular point are and ,corresponding to the two linearly independent solutions,See for precise conditions under which two Frobenius method yields two linearly independent solutions. If the exponents do not differ by an integer, this is always the case. and for expansion around the singular point they are and .
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This then determines the rest of the B_k. In some cases the constant must be zero. For example, consider the following differential equation (Kummer's equation with and ): :zu+(2-z)u'-u=0 The roots of the indicial equation are −1 and 0. Two independent solutions are 1/z and (e^z)/z, so we see that the logarithm does not appear in any solution.
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The equation should be studied on the Riemann sphere to include the point at infinity as a possible singular point. A Möbius transformation may be applied to move ∞ into the finite part of the complex plane if required, see example on Bessel differential equation below. Then the Frobenius method based on the indicial equation may be applied to find possible solutions that are power series times complex powers (z − a)r near any given a in the complex plane where r need not be an integer; this function may exist, therefore, only thanks to a branch cut extending out from a, or on a Riemann surface of some punctured disc around a. This presents no difficulty for a an ordinary point (Lazarus Fuchs 1866).
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