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1: 4.36 Infinite Products and Partial Fractions
§4.36 Infinite Products and Partial Fractions
2: 4.22 Infinite Products and Partial Fractions
§4.22 Infinite Products and Partial Fractions
3: 5.8 Infinite Products
§5.8 Infinite Products
4: 23.17 Elementary Properties
§23.17(iii) Infinite Products
5: 1.10 Functions of a Complex Variable
§1.10(ix) Infinite Products
M -test
Weierstrass Product
§1.10(x) Infinite Partial Fractions
6: 25.15 Dirichlet L -functions
25.15.2 L ( s , χ ) = p ( 1 - χ ( p ) p s ) - 1 , s > 1 ,
25.15.3 L ( s , χ ) = k - s r = 1 k - 1 χ ( r ) ζ ( s , r k ) ,
7: 20.5 Infinite Products and Related Results
§20.5 Infinite Products and Related Results
8: 25.2 Definition and Expansions
§25.2(iv) Infinite Products
25.2.11 ζ ( s ) = p ( 1 - p - s ) - 1 , s > 1 ,
25.2.12 ζ ( s ) = ( 2 π ) s e - s - ( γ s / 2 ) 2 ( s - 1 ) Γ ( 1 2 s + 1 ) ρ ( 1 - s ρ ) e s / ρ ,
9: 5.17 Barnes’ G -Function (Double Gamma Function)
5.17.2 G ( n ) = ( n - 2 ) ! ( n - 3 ) ! 1 ! , n = 2 , 3 , .
10: 23.8 Trigonometric Series and Products
§23.8(iii) Infinite Products