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relation to logarithmic integral

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1: 6.2 Definitions and Interrelations
The logarithmic integral is defined by …
2: 6.16 Mathematical Applications
If we assume Riemann’s hypothesis that all nonreal zeros of ζ ( s ) have real part of 1 2 25.10(i)), then …
3: 6.11 Relations to Other Functions
6.11.2 E 1 ( z ) = e z U ( 1 , 1 , z ) ,
4: 25.12 Polylogarithms
The special case z = 1 is the Riemann zeta function: ζ ( s ) = Li s ( 1 ) .
Integral Representation
Further properties include …and … In terms of polylogarithms …
5: 8.19 Generalized Exponential Integral
§8.19 Generalized Exponential Integral
§8.19(i) Definition and Integral Representations
§8.19(v) Recurrence Relation and Derivatives
§8.19(vi) Relation to Confluent Hypergeometric Function
§8.19(x) Integrals
6: 7.5 Interrelations
§7.5 Interrelations
7.5.13 G ( x ) = π F ( x ) 1 2 e x 2 Ei ( x 2 ) , x > 0 .
For Ei ( x ) see §6.2(i).
7: 7.18 Repeated Integrals of the Complementary Error Function
§7.18 Repeated Integrals of the Complementary Error Function
Hermite Polynomials
Confluent Hypergeometric Functions
Parabolic Cylinder Functions
Probability Functions
8: 12.7 Relations to Other Functions
§12.7 Relations to Other Functions
§12.7(i) Hermite Polynomials
§12.7(ii) Error Functions, Dawson’s Integral, and Probability Function
§12.7(iii) Modified Bessel Functions
§12.7(iv) Confluent Hypergeometric Functions
9: 19.10 Relations to Other Functions
§19.10 Relations to Other Functions
§19.10(i) Theta and Elliptic Functions
For relations of Legendre’s integrals to theta functions, Jacobian functions, and Weierstrass functions, see §§20.9(i), 22.15(ii), and 23.6(iv), respectively. …
§19.10(ii) Elementary Functions
In each case when y = 1 , the quantity multiplying R C supplies the asymptotic behavior of the left-hand side as the left-hand side tends to 0. …
10: 7.10 Derivatives
§7.10 Derivatives
7.10.1 d n + 1 erf z d z n + 1 = ( 1 ) n 2 π H n ( z ) e z 2 , n = 0 , 1 , 2 , .
7.10.2 w ( z ) = 2 z w ( z ) + ( 2 i / π ) ,
d g ( z ) d z = π z f ( z ) 1 .