A More General Treatment of Linear Differential Equations of the Second Order with Non-analytic Coefficients and One Regular Singular Point, the Independent Variable Being1902 - Differential equations, Linear - 21 pages |
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¹ ƒ approximation-differences Bôcher's interval Bôcher's paper Choose C₁ continuous function thr continuous thr defined denote dx must vanish dx² E₁ E₁(x E₂ E₂(a E₂(x equal exponents exponents are equal exponents are unequal final solution-theorems following result formulas 15 fulfilled Furthermore H₁ H₁(a H₁(x H₂(a H₂(x hence I'dx I₁ I₁(a immediately from 9 INDEPENDENT VARIABLE inequalities 11 integrable integrable to x interval of validity IRA STERNER J₁ J₂ LINEAR DIFFERENTIAL EQUATIONS log x log x-a log² moreover n=1 applying 14 N₂ NON-ANALYTIC COEFFICIENTS ORDER WITH NON-ANALYTIC P₁ pair of conditions PICARD'S method positive constants positive function q₁ REAL BY IRA regular singular point Remembering SECOND ORDER second solution series 13 sole necessary condition sufficient conditions test-series uniformly convergent thr uniformly convergent throughout VARIABLE BEING REAL write Y₁ Y₁₁ Y₂ Þ x ΣΥ знах