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Alexandre
Alexandre
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I am interested in the series $$\sum_{n\geq 1}I_n(x)\lambda^n$$ which is not the full generating series of the modified Bessel function of the first kind because it startstarts from $n=1$ and not at $-\infty$. If we can not find a closed form for this series, what relevant information can we extract from it?

I am interested in the series $$\sum_{n\geq 1}I_n(x)\lambda^n$$ which is not the full generating series of the modified Bessel function of the first kind because it start from $n=1$ and not at $-\infty$. If we can not find a closed form for this series, what relevant information can we extract from it?

I am interested in the series $$\sum_{n\geq 1}I_n(x)\lambda^n$$ which is not the full generating series of the modified Bessel function of the first kind because it starts from $n=1$ and not at $-\infty$. If we can not find a closed form for this series, what relevant information can we extract from it?

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YCor
YCor
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Alexandre
Alexandre
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What can we know about "the half" of the generating series of Bessel function

I am interested in the series $$\sum_{n\geq 1}I_n(x)\lambda^n$$ which is not the full generating series of the modified Bessel function of the first kind because it start from $n=1$ and not at $-\infty$. If we can not find a closed form for this series, what relevant information can we extract from it?