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Notations F

*ABCDE♦F♦GHIJKLMNOPQRSTUVWXYZ
Fn
Fibonacci number; 26.11
FD
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)
Fν(z)=Meν(z,q)
notation used by Abramowitz and Stegun (1964, Chapter 20); 28.1
(with Meν(z,q): modified Mathieu function)
Fs(x)
Fermi–Dirac integral; (25.12.14)
Fc(x)
Fourier cosine transform; (1.14.9)
Fs(x)
Fourier sine transform; (1.14.10)
Fp(z)
terminant function; (8.22.1)
fe,m(h)
joining factor for radial Mathieu functions; 28.22(i)
fo,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,bc;z)
hypergeometric function; 15.1
F(a,b;c;z)
hypergeometric function; (15.2.1)
F(a,bc;z)
Olver’s hypergeometric function; 15.1
F(a,b;c;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(ab;T)
confluent hypergeometric function of matrix argument (first kind); 35.6(i)
F11(a;b;T)
confluent hypergeometric function of matrix argument (first kind); 35.1
F11(a;b;T)
confluent hypergeometric function of matrix argument (first kind); 35.6(i)
F12(a,bc;T)
hypergeometric function of matrix argument; 35.7(i)
F12(a,b;c;T)
hypergeometric function of matrix argument; 35.1
F12(a,b;c;T)
hypergeometric function of matrix argument; 35.7(i)
F12(a,b;c;z)
hypergeometric function; 15.1
Fqp(ab;z)
generalized hypergeometric function; (16.2.1)
Fqp(ab;z)
generalized hypergeometric function; 16.5
Fqp(a1,,apb1,,bq;z)
generalized hypergeometric function; (16.2.1)
Fqp(a1,,apb1,,bq;z)
generalized hypergeometric function; 16.5
Fqp(a1,a2,,apb1,b2,,bq;T)
generalized hypergeometric function of matrix argument; 35.8(i)
Fqp(a;b;z)
generalized hypergeometric function; (16.2.1)
Fqp(a;b;z)
generalized hypergeometric function; 16.5
Fqp(a1,,ap;b1,,bq;z)
generalized hypergeometric function; (16.2.1)
Fqp(a1,,ap;b1,,bq;z)
generalized hypergeometric function; 16.5
Fqp(a1,a2,,ap;b1,b2,,bq;T)
generalized hypergeometric function of matrix argument; 35.1
Fqp(a1,a2,,ap;b1,b2,,bq;T)
generalized hypergeometric function of matrix argument; 35.8(i)
F12(a,b;c;z)
Olver’s hypergeometric function; 15.1
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
F1(α;β,β;γ;x,y)
Appell function; (16.13.1)
F2(α;β,β;γ,γ;x,y)
Appell function; (16.13.2)
F3(α,α;β,β;γ;x,y)
Appell function; (16.13.3)
F4(α;β;γ,γ;x,y)
Appell function; (16.13.4)
Fcm(z,h)
Mathieu function; 28.26(i)
Fen(z,q)
modified Mathieu function; (28.20.6)
fen(z,q)
second solution, Mathieu’s equation; (28.5.1)
Feyn(z,q)=12πge,n(h)cen(0,q)Mcn(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)
Fsm(z,h)
Mathieu function; 28.26(i)