Sorry, I gave a moronic answer before. Let me try to give a better one.
There should be no expression for f(lambda):=sumkgeq1lambdak/(k2k!) in elementary functions. If there were, then g(lambda)=lambdaf′(lambda)=sumkgeq1lambdak/(kcdotk!) would also be elementary. But g(lambda)=intlambda0fracet−1tdt and et/t is a standard example of a function without an elementary antiderivative.
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