A Few Beautiful Applications
In the formulas below G is Catalan's constant, γ is the Euler's constant, β2n is the Bernoulli number of order 2n, H2n+1 is the harmonic number of order 2n+1 and Ei is the Exponential integral function.
The notation indicating the 2 periodic function coinciding with on (−1, 1).
If the measure ρ is reducible and let φ be the associated reducer, one has the equality
If the measure ρ is reducible with μ the associated reducer, then if f is square integrable for μ, and if g is square integrable for ρ and is orthogonal with P0 = 1 one has equivalence:
c1 indicates the moment of order 1 of ρ and Tρ the operator
Read more about this topic: Secondary Measure
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“All round and round does the world lie as in a sharp-shooter’s ambush, to pick off the beautiful illusions of youth, by the pitiless cracking rifles of the realities of age.”
—Herman Melville (1819–1891)