Phi (/faɪ/; uppercase Φ, lowercase φ or ϕ; Ancient Greek: ϕεῖ pheî [pʰéî̯]; Modern Greek: φι fi [fi]) is the twenty-first letter of the Greek alphabet...

ᴺ ᴻ ᴼ ᴽ ᴾ ᴿ ᵀ ᵁ ᵂ ᵃ ᵄ ᵅ ᵆ ᵇ ᵈ ᵉ ᵊ ᵋ ᵌ ᵍ ᵏ ᵐ ᵑ ᵒ ᵓ ᵖ ᵗ ᵘ ᵚ ᵛ, Greek ᵝ ᵞ ᵟ ᵠ ᵡ, Cyrillic ᵸ, other ᵎ ᵔ ᵕ ᵙ ᵜ. These are intended to indicate secondary articulation...

prime to n. It is written using the Greek letter phi as φ ( n ) {\displaystyle \varphi (n)} or ϕ ( n ) {\displaystyle \phi (n)} , and may also be called...

latitude ϕ to the equator is given by (ϕ in radians) m ( ϕ ) = ∫ 0 ϕ M ( ϕ ′ ) d ϕ ′ = a ( 1 − e 2 ) ∫ 0 ϕ ( 1 − e 2 sin 2 ⁡ ϕ ′ ) − 3 2 d ϕ ′ {\displaystyle...

a linear expression, as in: 3 φ 3 − 5 φ 2 + 4 = 3 ( φ 2 + φ ) − 5 φ 2 + 4 = 3 [ ( φ + 1 ) + φ ] − 5 ( φ + 1 ) + 4 = φ + 2 ≈ 3.618033. {\displaystyle...

cos ⁡ φ x ^ + sin ⁡ θ sin ⁡ φ y ^ + cos ⁡ θ z ^ , θ ^ = cos ⁡ θ cos ⁡ φ x ^ + cos ⁡ θ sin ⁡ φ y ^ − sin ⁡ θ z ^ , φ ^ = − sin ⁡ φ x ^ + cos ⁡ φ y ^ {\displaystyle...

A ϕ ( z ) ( ρ + d ρ ) d ϕ − A ϕ ( z + d z ) ( ρ + d ρ ) d ϕ + A z ( ϕ + d ϕ ) d z − A z ( ϕ ) d z ( ρ + d ρ ) d ϕ d z = − ∂ A ϕ ∂ z + 1 ρ ∂ A z ∂ ϕ {\displaystyle...

induction on n ≥ 1: φ n + 1 = ( F n φ + F n − 1 ) φ = F n φ 2 + F n − 1 φ = F n ( φ + 1 ) + F n − 1 φ = ( F n + F n − 1 ) φ + F n = F n + 1 φ + F n . {\displaystyle...

the following form: if X is a random variable and φ is a convex function, then φ ( E ⁡ [ X ] ) ≤ E ⁡ [ φ ( X ) ] . {\displaystyle \varphi (\operatorname...

2nd projection map) and for any x in X: Φ ( 0 , x ) = x {\displaystyle \Phi (0,x)=x} Φ ( t 2 , Φ ( t 1 , x ) ) = Φ ( t 2 + t 1 , x ) , {\displaystyle \Phi...

the free dictionary. Phi (Φ, φ, or ϕ) is the 21st letter of the Greek alphabet. Phi or PHI may also refer to: Golden ratio (φ) Phi coefficient, a measure...

whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it...

cos ⁡ φ ,   sin ⁡ φ ) + 2 r ˙ φ ˙ ( − sin ⁡ φ ,   cos ⁡ φ ) + r φ ¨ ( − sin ⁡ φ ,   cos ⁡ φ ) − r φ ˙ 2 ( cos ⁡ φ ,   sin ⁡ φ ) = ( r ¨ − r φ ˙ 2 ) r...

√5/2⁠ ≈ 1.61803399 symbolized by the Greek letter φ) as its base. It is sometimes referred to as base-φ, golden mean base, phi-base, or, colloquially, phinary...

δ ′ , φ ⟩ = ⟨ δ ′ , x φ ⟩ = − ⟨ δ , ( x φ ) ′ ⟩ = − ⟨ δ , x ′ φ + x φ ′ ⟩ = − ⟨ δ , x ′ φ ⟩ − ⟨ δ , x φ ′ ⟩ = − x ′ ( 0 ) φ ( 0 ) − x ( 0 ) φ ′ ( 0 )...

when at latitude ϕ), is about 111132.92 − 559.82 cos ⁡ 2 ϕ + 1.175 cos ⁡ 4 ϕ − 0.0023 cos ⁡ 6 ϕ {\displaystyle 111132.92-559.82\,\cos 2\phi +1.175\,\cos...

connectives, is this single clause: ϕ ::= a 1 , a 2 , …   |   ¬ ϕ   |   ϕ   &   ψ   |   ϕ ∨ ψ   |   ϕ → ψ   |   ϕ ↔ ψ {\displaystyle \phi ::=a_{1},a_{2}...

φ φ ^ + ∂ f ∂ z z ^ ∇ ⋅ A = 1 ρ ∂ ∂ ρ ( ρ A ρ ) + 1 ρ ∂ A φ ∂ φ + ∂ A z ∂ z ∇ × A = ( 1 ρ ∂ A z ∂ φ − ∂ A φ ∂ z ) ρ ^ + ( ∂ A ρ ∂ z − ∂ A z ∂ ρ ) φ ^...

In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F {\displaystyle F} of some real variable t {\displaystyle t}...

w_{n}\right)\in H,} φ ( w ) = φ 1 w 1 + ⋯ + φ n w n = [ φ 1 , … , φ n ] [ w 1 ⋮ w n ] = [ φ 1 ¯ ⋮ φ n ¯ ] ¯ T w → = f φ → ¯ T w → = ⟨ f φ ∣ w ⟩ , {\displaystyle...

, x μ ) − L ( φ A , φ A , ν , x μ ) ] = ∂ ∂ x σ ( ∂ L ∂ φ A , σ ) δ ¯ φ A + ∂ L ∂ φ A , σ δ ¯ φ A , σ = ∂ ∂ x σ ( ∂ L ∂ φ A , σ δ ¯ φ A ) . {\displaystyle...

\varphi .\end{aligned}}} J F ( r , φ ) = [ ∂ x ∂ r ∂ x ∂ φ ∂ y ∂ r ∂ y ∂ φ ] = [ cos ⁡ φ − r sin ⁡ φ sin ⁡ φ r cos ⁡ φ ] {\displaystyle \mathbf {J} _{\mathbf...

spiral r = a φ n {\displaystyle r=a\varphi ^{n}\;} the length is L = ∫ φ 1 φ 2 n 2 r 2 φ 2 + r 2 d φ = a ∫ φ 1 φ 2 φ n − 1 n 2 + φ 2 d φ   . {\displaystyle...

function φ {\textstyle \varphi } whose value depends only on the distance between the input and some fixed point, either the origin, so that φ ( x ) = φ ^ (...

cos ⁡ ( φ 1 ) cos ⁡ ( φ 2 ) + sin ⁡ ( φ 1 ) sin ⁡ ( φ 2 ) = sin ⁡ ( φ 2 ) sin ⁡ ( φ 1 ) + cos ⁡ ( φ 2 ) cos ⁡ ( φ 1 ) − cos ⁡ ( φ 2 ) cos ⁡ ( φ 1 ) + cos...

Φ ( 0 ) ( x 0 ) = 1 2 π ∫ − ∞ x 0 e − t 2 / 2 d t Φ ( 1 ) ( x 0 ) = 1 2 π e − x 0 2 / 2 Φ ( n ) ( x 0 ) = − ( x 0 Φ ( n − 1 ) ( x 0 ) + ( n − 2 ) Φ (...

free in ¬φ if and only if x occurs free in φ. x occurs bound in ¬φ if and only if x occurs bound in φ Binary connectives x occurs free in (φ → ψ) if and...

1 − φ 1 z − 1 − φ 2 z − 2 = 0 {\displaystyle 1-\varphi _{1}z^{-1}-\varphi _{2}z^{-2}=0} , which yields: z 1 , z 2 = 1 2 φ 2 ( φ 1 ± φ 1 2 + 4 φ 2 ) {\displaystyle...

{\displaystyle {\tfrac {1+{\sqrt {5}}}{2}}:1,} or ⁠ φ : 1 , {\displaystyle \varphi :1,} ⁠ with ⁠ φ {\displaystyle \varphi } ⁠ approximately equal to 1...

this would require that ϕ α ∘ Φ ∘ ϕ β − 1 {\displaystyle \phi _{\alpha }\circ \Phi \circ \phi _{\beta }^{-1}} and ϕ α ∘ Φ − 1 ∘ ϕ β − 1 {\displaystyle \phi...