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convert/hypergeom - convert functions in an expression to hypergeometric form
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Calling Sequence
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convert( expr, hypergeom, opt_1, opt_2,  )
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Description
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Converts the functions found in expr, including sum and Sum, to their hypergeometric forms when possible. For sums, no attempt is made to ensure that the resulting hypergeometric function is convergent or terminates.
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Examples
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| (2) |
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| (3) |
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![BesselJ(a, z) = z^a*hypergeom([], [1+a], -(1/4)*z^2)/(GAMMA(1+a)*2^a)](/support/helpjp/helpview.aspx?si=6535/file03664/math92.png)
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| (5) |
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![LegendreP(a, b, z) = (z+1)^((1/2)*b)*hypergeom([-a, 1+a], [1-b], 1/2-(1/2)*z)/((z-1)^((1/2)*b)*GAMMA(1-b))](/support/helpjp/helpview.aspx?si=6535/file03664/math106.png)
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![KummerU(a, b, z) = GAMMA(-1+b)*hypergeom([a-b+1], [2-b], z)/(z^(-1+b)*GAMMA(a))+GAMMA(1-b)*hypergeom([a], [b], z)/GAMMA(a-b+1)](/support/helpjp/helpview.aspx?si=6535/file03664/math120.png)
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For negative a we have
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![`assuming`([KummerU(a, b, z) = convert(KummerU(a, b, z), hypergeom)], [a::negint])](/support/helpjp/helpview.aspx?si=6535/file03664/math128.png)
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![KummerU(a, b, z) = pochhammer(a-b+1, -a)*hypergeom([a], [b], z)](/support/helpjp/helpview.aspx?si=6535/file03664/math131.png)
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Elementary functions are not converted by default (see convert[to_special_function])
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To convert them use any of the optional arguments: include=elementary, or include=all
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| (11) |
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![sin(z) = z*hypergeom([], [3/2], -(1/4)*z^2)](/support/helpjp/helpview.aspx?si=6535/file03664/math162.png)
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