Unformatted text preview: answer should depend on the value of s . 4. Property of the Gaussian hypergeometric function. Denoting the Gaussian hypergeometric function by F ( α, β, γ ; x ), show that ln(1 + x ) = xF (1 , 1 , 2;-x ) . 5. Properties of Bessel functions. Denoting the Bessel function of the ±rst kind of order ν > 0 by J ν ( x ), show that the following properties hold: d dx ( x − ν J ν ( x ) ) =-x − ν J ν +1 ( x ) and J ν +1 ( x ) = 2 ν x J ν ( x )-J ν − 1 ( x ) . * MAP 4305; Instructor: Patrick De Leenheer. 1...
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- Summer '06
- linearly independent solutions, Bessel function, Special functions, Hypergeometric series, Gaussian hypergeometric function