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Regular Singular Points

Regular Singular Points. If cither of the functions a(a ), fi x) is not analytic at the point x = a, wc say that this point is a singular point of the differential equation. When the functions a ir), f)(x) are of such a nature that the differential equation may be written in the form... [Pg.6]

If x = a is a regular singular point of the equation (3.1) it can he shown that there exists at least one solution of the form ... [Pg.6]

Tiius the regular singular points of the hypcrgcometrie equation are -... [Pg.25]

We shall now consider the form of the solutions in the neighbourhood of tile regular singular points. [Pg.25]

Since Legendre s equation has a regular singular point at ft = 1 we nmy on the basis of equation (3.8) take the... [Pg.64]

Here, the familiar eigenvalues of the orbital angular momentum operators have already been incorporated, reminding the reader that their form and numerical values are determined by the periodicity condition + 2n) = (0) for the first one, and by guaranteeing good behavior for the second at its regular singularity points, 9 = 0 and n. [Pg.92]

For regular singular points, a series solution of the differential equation can be obtained by the method of Frobenius. This is based on the following generalization of the power series expansion ... [Pg.154]

Series Solutions Near a Regular Singular Point... [Pg.61]

In Section 3.5.1, the Frobenius series method was discussed with regard to differential equations with regular singular points. In this section, a method is given that effectively deals with differential equations with ordinary points. To illustrate the importance of this method consider the relatively harmless-looking first-order initial value problem... [Pg.83]


See other pages where Regular Singular Points is mentioned: [Pg.6]    [Pg.10]    [Pg.24]    [Pg.61]    [Pg.61]    [Pg.103]    [Pg.265]    [Pg.93]    [Pg.154]    [Pg.154]    [Pg.61]    [Pg.62]    [Pg.65]    [Pg.69]    [Pg.69]   
See also in sourсe #XX -- [ Pg.154 ]

See also in sourсe #XX -- [ Pg.61 ]




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Regular points

Series Solutions Near a Regular Singular Point

Singular

Singular points

Singularities

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