Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.akxq)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=7/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=7/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.akxq.01

Input Form

HypergeometricPFQ[{7/2, 7/2}, {-(11/2), 3}, z] == (1/2338875) (4 E^(z/2) (1091475 - 827820 z + 436860 z^2 - 230400 z^3 + 147600 z^4 - 141120 z^5 + 360192 z^6 + 774144 z^7 + 264960 z^8 + 29696 z^9 + 1024 z^10) BesselI[0, z/2]) + (1/(2338875 z)) (4 E^(z/2) (-2027025 + 405405 z + 180360 z^2 - 201060 z^3 + 133200 z^4 - 87120 z^5 + 71232 z^6 - 97536 z^7 + 550656 z^8 + 236800 z^9 + 28672 z^10 + 1024 z^11) 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]