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

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=-9/2

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

Input Form

HypergeometricPFQ[{7/2, 7/2}, {-(9/2), 5}, z] == -((1/(70875 z^2)) (32 E^(z/2) (-103378275 + 50675625 z - 15656760 z^2 + 3616200 z^3 - 671760 z^4 + 104880 z^5 - 14400 z^6 + 2496 z^7 + 1280 z^8 + 256 z^9) BesselI[0, z/2])) - (1/(70875 z^3)) (32 E^(z/2) (413513100 - 202702500 z + 75540465 z^2 - 20790000 z^3 + 4503960 z^4 - 802560 z^5 + 121200 z^6 - 15744 z^7 + 1600 z^8 + 1024 z^9 + 256 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]