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Notations F

*ABCDE♦F♦GHIJKLMNOPQRSTUVWXYZ
F n
Fibonacci number; §26.11
F D
Lauricella’s multivariate hypergeometric function; §19.15
F ( x )
Fourier transform; 1.14.1
F ( z )
Dawson’s integral; 7.2.5
( z )
Fresnel integral; 7.2.6
F ( z - 1 ) = ψ ( z )
notation used by Pairman (1919); §5.1
(with ψ(z): psi (or digamma) function)
f ( x )
Euler’s reciprocal function; 27.14.2
f ( z )
auxiliary function for sine and cosine integrals; 6.2.17
f ( z )
auxiliary function for Fresnel integrals; 7.2.10
F ν ( z ) = Me ν ( z , q )
notation used by Abramowitz and Stegun (1964, Chapter 20); §28.1
(with Meν(z,q): modified Mathieu function)
F s ( x )
Fermi–Dirac integral; 25.12.14
F c ( x )
Fourier cosine transform; 1.14.9
F s ( x )
Fourier sine transform; 1.14.10
F p ( z )
terminant function; 2.11.11
f e , m ( h )
joining factor for radial Mathieu functions; §28.22(i)
f o , m ( h )
joining factor for radial Mathieu functions; §28.22(i)
F ( ϕ \ α ) = F ( ϕ , k )
notation used by Abramowitz and Stegun (1964, Chapter 17); §19.1
(with F(ϕ,k): Legendre’s incomplete elliptic integral of the first kind)
F ( ϕ , k )
Legendre’s incomplete elliptic integral of the first kind; 19.2.4
F ( x , s )
periodic zeta function; 25.13.1
F ( η , ρ )
regular Coulomb radial function; 33.2.3
F(a,b;c;z) or F(a,bc;z)
hypergeometric function; 15.2.1
F(a,b;c;z) or F(a,bc;z)
Olver’s hypergeometric function; 15.2.2
f ( ϵ , ; r ) = s ( ϵ , ; r )
notation used by Greene et al. (1979); Greene et al. (1979):
(with s(ϵ,;r): regular Coulomb function)
f ( ϵ , ; r )
regular Coulomb function; 33.14.4
f ( 0 ) ( ϵ , ; r ) = f ( ϵ , ; r )
notation used by Greene et al. (1979); Greene et al. (1979):
(with f(ϵ,;r): regular Coulomb function)
F11(a;b;T) or F11(ab;T)
confluent hypergeometric function of matrix argument (first kind); 35.6.1
F12(a,b;c;z) or F12(a,bc;z)
hypergeometric function; 15.2.1
F12(a,b;c;T) or F12(a,bc;T)
hypergeometric function of matrix argument; §35.7(i)
F 1 2 ( a , b ; c ; z )
Olver’s hypergeometric function; 15.2.2
Fqp(a1,,ap;b1,,bq;z), or Fqp(a1,,apb1,,bq;z)
alternatively Fqp(a;b;z) or Fqp(ab;z)
generalized hypergeometric function; §16.2
Fqp(a1,,ap;b1,,bq;T) or Fqp(a1,,apb1,,bq;T)
generalized hypergeometric function of matrix argument; §35.8(i)
Fqp(a;b;z) or Fqp(ab;z)
scaled (or Olver’s) generalized hypergeometric function; 16.2.5
F ( a , b ; t : q )
alternative notation for specialization of ϕ12; Fine (1988); §17.1
F 1 ( α ; β , β ; γ ; x , y )
first Appell function; 16.13.1
F 2 ( α ; β , β ; γ , γ ; x , y )
second Appell function; 16.13.2
F 3 ( α , α ; β , β ; γ ; x , y )
third Appell function; 16.13.3
F 4 ( α ; β ; γ , γ ; x , y )
fourth Appell function; 16.13.4
Fc m ( z , h )
Mathieu function; §28.26(i)
Fe n ( z , q )
modified Mathieu function; 28.20.6
fe n ( z , q )
second solution, Mathieu’s equation; 28.5.1
Fey n ( z , q ) = 1 2 π g e , n ( h ) ce n ( 0 , q ) Mc n ( 2 ) ( z , h )
notation used by Arscott (1964b), McLachlan (1947); §28.1
(with cen(z,q): Mathieu function and Mcn(j)(z,h): radial Mathieu function)
Fs m ( z , h )
Mathieu function; §28.26(i)