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NIST
Notations

Notations F

*ABCDE♦F♦GHIJKLMNOPQRSTUVWXYZ
F D
Lauricella’s multivariate hypergeometric function; §19.15
F n
Fibonacci number; §26.11
f ( x )
Euler’s reciprocal function; (27.14.2)
f ( z )
auxiliary function for Fresnel integrals; (7.2.10)
f ( z )
auxiliary function for sine and cosine integrals; (6.2.17)
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 e , m ( h )
joining factor for radial Mathieu functions; §28.22(i)
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 o , m ( h )
joining factor for radial Mathieu functions; §28.22(i)
F p ( z )
terminant function; (2.11.11)
F s ( x )
Fermi–Dirac integral; (25.12.14)
( f ) ( s )
Fourier transform; (1.14.1)
c ( f ) ( s )
Fourier cosine transform; (1.14.9)
s ( f ) ( s )
Fourier sine transform; (1.14.10)
( u )
Fourier transform of a tempered distribution; (1.16.35)
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 ( η , ρ )
regular Coulomb radial function; (33.2.3)
F ( x , s )
periodic zeta function; (25.13.1)
F(a,b;c;z) or F(a,bc;z)
=F12(a,b;c;z) Gauss’ 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); item Greene et al. (1979):
(with s(ϵ,;r): regular Coulomb function)
f ( ϵ , ; r )
regular Coulomb function; (33.14.4)
F 1 1 ( a ; b ; z )
=M(a,b,z) notation for the Kummer confluent hypergeometric function; §16.2
F11(a;b;T) or F11(ab;T)
confluent hypergeometric function of matrix argument (first kind); §35.6(i)
F 1 2 ( a , b ; c ; z )
=F(a,b;c;z) notation for Gauss’ hypergeometric function; §16.2
F12(a,b;c;T) or F12(a,bc;T)
Gaussian hypergeometric function of matrix argument; (35.7.1)
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(a;b;z) or Fqp(ab;z)
scaled (or Olver’s) generalized hypergeometric function; (16.2.5)
Fqp(a1,,ap;b1,,bq;T) or Fqp(a1,,apb1,,bq;T)
generalized hypergeometric function of matrix argument; (35.8.1)
f ( 0 ) ( ϵ , ; r ) = f ( ϵ , ; r )
notation used by Greene et al. (1979); item Greene et al. (1979):
(with f(ϵ,;r): regular Coulomb function)
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)
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, π: the ratio of the circumference of a circle to its diameter and Mcn(j)(z,h): radial Mathieu function)