What is $\,_1F_1(0;0;x)$? Since its first argument is $0$, either we say it is 0 or since its first and second arguments are equal we say it is $e^x$? I cannot understand.
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The function is constant: $$ \,_1F_{1}(0;0;x) = 1 $$
The exponential form comes from $$ \,_1F_{1}(1;1;x) = e^{x} $$
Note the special case you ask about:
You have focused on a special case of $b=0$. From WolframMathworl:
dantopa
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Thanks but how can we prove it? – LİLA Apr 03 '17 at 15:06
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@LİLA: Prove the 0 result or the exponential result? – dantopa Apr 03 '17 at 15:16
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Proof of the 0 result? – LİLA Apr 03 '17 at 15:20