Strange behavior of hypergeometric function in maple

Discussion in 'Maple' started by lex, Nov 8, 2014.

  1. lex

    lex

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    I cosider (finite) hypergemetric series for 2F1 satisfying Kummer's identuty at z=-1 . Depending on

    1. evaluation it by hypergeometric 2F1[a,b,a-b+1]
    2. or Kummer identity
    GAMMA(a-b+1)*GAMMA(1+(1/2)*a) / (GAMMA(a+1)*GAMMA(1+(1/2)*a-b))

    or using pochgammer symbol notation:

    pochhammer(1+(1/2)*a-b, (1/2)*a)/pochhammer(1+(1/2)*a, (1/2)*a)

    I get copletely different answers. Perhaps anybody knows what might be the problem?

    CODE:

    eval(hypergeom([a, b], [a-b+1], -1), [a = -2, b = -4])

    OBTAIN -2/3

    eval(pochhammer(1+(1/2)*a-b, (1/2)*a)/pochhammer(1+(1/2)*a, (1/2)*a), [a = -2, b = -4])

    OBTAIN

    -1/3

    BUT (this is in fact Kummer's identity):

    simplify(pochhammer(1+(1/2)*a-b, (1/2)*a)/pochhammer(1+(1/2)*a, (1/2)*a)-hypergeom([a, b], [a-b+1], -1), 'symbolic' );

    OBTAIN
    0
     
    Last edited: Nov 8, 2014
    lex, Nov 8, 2014
    #1
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