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## Main Question or Discussion Point

given a probability distribution P(x) >0 on a given interval , if we define the moment generatign function

[tex] M(x)= \int_{a}^{b}dt e^{xt}P(t)dt [/tex]

my question is , if the moment problem is determined, then could we say that ALL the zeros of M(x) are PURELY imaginary ? [tex] ia [/tex] or this is only for certain P(x) ??

[tex] M(x)= \int_{a}^{b}dt e^{xt}P(t)dt [/tex]

my question is , if the moment problem is determined, then could we say that ALL the zeros of M(x) are PURELY imaginary ? [tex] ia [/tex] or this is only for certain P(x) ??