Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5806)

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/07.25.03.5806.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2)}, {-(9/2), 6}, z] == (1/(20675655 z^3)) (32 E^(z/2) (47880 + 67095 z + 62370 z^2 + 702660 z^3 - 540960 z^4 + 112752 z^5 - 7712 z^6 + 128 z^7) BesselI[0, z/2]) - (1/(20675655 z^4)) (32 E^(z/2) (191520 + 268380 z + 255465 z^2 + 234570 z^3 + 308700 z^4 - 439392 z^5 + 105232 z^6 - 7584 z^7 + 128 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]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]