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as Solution of j m iL+if 1 y0 101
Lemma relating to functional dependence
72 other sections not shown
arbitrary constant arbitrary function ascending powers assume Bessel's equation complementary function Complete Integral consider converging converging series corresponding definite integrals denoted dependent derived differential coefficients dy dx elimination equal equation becomes equation giving equation is satisfied equations dx equivalent example expansions in ascending expressed in terms factor finite form finite terms foregoing Frobenius method Hence hypergeometric series independent variable indicated indicial equation integrable in finite integral equation latter left-hand side Legendre's equation linear equation locus method multiplied Obtain the primitive occur original equation orthogonal trajectory partial differential equation Particular Integral perfect differential positive integer proceed Prove quantities regular integral relation result Riccati's equation right-hand side roots satisfy the equation second order Shew simultaneous equations sin8 singular solution Solve the equations substituted suppose system of curves tangent term involving theorem transformed unity vanish write zero