Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3799)

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=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=1, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=1, b₁=4

http://functions.wolfram.com/07.25.03.3799.01

Input Form

HypergeometricPFQ[{-(9/2), 1}, {4, 5}, z] == (24 (16 - 60 z + 65 z^2))/(715 z^3) - (1/(8212829625 z^3)) (128 E^(z/2) (34459425 - 145945800 z + 193393080 z^2 - 112461840 z^3 + 32713200 z^4 - 5031360 z^5 + 409920 z^6 - 16512 z^7 + 256 z^8) BesselI[0, z/2]) + (1/(8212829625 z^3)) (128 E^(z/2) (2027025 - 53453880 z + 117719640 z^2 - 86189040 z^3 + 28249200 z^4 - 4645440 z^5 + 393792 z^6 - 16256 z^7 + 256 z^8) 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]
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