Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9227)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=1, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=1, b₁=5

http://functions.wolfram.com/07.25.03.9227.01

Input Form

HypergeometricPFQ[{-(5/2), 1}, {5, 5}, z] == (32 (-32 + 208 z - 286 z^2 + 143 z^3))/(1001 z^4) - (1/(135270135 z^4)) (1024 E^(z/2) (-135135 + 945945 z - 1589352 z^2 + 1035384 z^3 - 305520 z^4 + 42896 z^5 - 2752 z^6 + 64 z^7) BesselI[0, z/2]) + (1/(135270135 z^3)) (1024 E^(z/2) (264207 - 903504 z + 786456 z^2 - 266560 z^3 + 40240 z^4 - 2688 z^5 + 64 z^6) BesselI[1, z/2])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]