Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0816)

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=-11/2, a₂>=-11/2

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

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

http://functions.wolfram.com/07.25.03.0816.01

Input Form

HypergeometricPFQ[{-(11/2), 1/2}, {-(5/2), 6}, z] == -((1/(4583103525 z^3)) (32 E^(z/2) (-178378200 - 191756565 z - 126922950 z^2 - 215093340 z^3 - 2328480 z^4 - 1688400 z^5 - 3382176 z^6 + 5746560 z^7 - 976896 z^8 + 40960 z^9) BesselI[0, z/2])) + (1/(4583103525 z^4)) (32 E^(z/2) (-713512800 - 767026260 z - 529989075 z^2 - 311454990 z^3 - 206361540 z^4 + 1562400 z^5 + 941136 z^6 + 1021920 z^7 + 4831104 z^8 - 935936 z^9 + 40960 z^10) 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]