Shannon's Noiseless Coding Theorem

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5th minterm in 3 variables
gamma(x) integral representation
integrate sqrt( (1+x^2)/(1+x^4) ) dx, x=0..1

References

Let

be an information source with entropy

. ThenH(S)<=m(S),where

is the minimum average code-word length among all uniquely decipherable coding schemes for

ReferencesCasti, J. L. "The Shannon Coding Theorem." Ch. 1 in Five More Golden Rules: Knots, Codes, Chaos, and Other Great Theories of 20th-Century Mathematics. New York: Wiley, pp. 207-254, 2000.