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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(5/2), 6}, z] == -((1/(893025 z^3)) (32 E^(z/2) (-48648600 + 23918895 z - 7422030 z^2 + 1689660 z^3 - 252000 z^4 - 85680 z^5 + 570528 z^6 + 1890048 z^7 + 1281024 z^8 + 317184 z^9 + 31232 z^10 + 1024 z^11) BesselI[0, z/2])) - (1/(893025 z^4)) (32 E^(z/2) (194594400 - 95675580 z + 35769195 z^2 - 9860130 z^3 + 2153340 z^4 - 413280 z^5 + 111888 z^6 - 131232 z^7 + 999168 z^8 + 1007616 z^9 + 287488 z^10 + 30208 z^11 + 1024 z^12) 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]