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1: 16.7 Relations to Other Functions
§16.7 Relations to Other Functions
2: 6.11 Relations to Other Functions
§6.11 Relations to Other Functions
Incomplete Gamma Function
Confluent Hypergeometric Function
6.11.2 E 1 ( z ) = e - z U ( 1 , 1 , z ) ,
3: 19.10 Relations to Other Functions
§19.10 Relations to Other Functions
§19.10(i) Theta and Elliptic Functions
§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. For relations to the Gudermannian function gd ( x ) and its inverse gd - 1 ( x ) 4.23(viii)), see (19.6.8) and …
4: 25.17 Physical Applications
§25.17 Physical Applications
This relates to a suggestion of Hilbert and Pólya that the zeros are eigenvalues of some operator, and the Riemann hypothesis is true if that operator is Hermitian. …
5: 16.24 Physical Applications
§16.24(iii) 3 j , 6 j , and 9 j Symbols
The coefficients of transformations between different coupling schemes of three angular momenta are related to the Wigner 6 j symbols. …
6: 13.18 Relations to Other Functions
§13.18 Relations to Other Functions
§13.18(ii) Incomplete Gamma Functions
§13.18(iv) Parabolic Cylinder Functions
§13.18(v) Orthogonal Polynomials
Laguerre Polynomials
7: 25.13 Periodic Zeta Function
§25.13 Periodic Zeta Function
The notation F ( x , s ) is used for the polylogarithm Li s ( e 2 π i x ) with x real: … Also, …
8: 7.11 Relations to Other Functions
§7.11 Relations to Other Functions
Incomplete Gamma Functions and Generalized Exponential Integral
Confluent Hypergeometric Functions
Generalized Hypergeometric Functions
9: 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
10: 10.39 Relations to Other Functions
§10.39 Relations to Other Functions
Elementary Functions
Parabolic Cylinder Functions
Confluent Hypergeometric Functions
Generalized Hypergeometric Functions and Hypergeometric Function