Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ah6e)

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=3/2, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.ah6e.01

Input Form

HypergeometricPFQ[{3/2, 11/2}, {-(11/2), 6}, z] == (1/(654885 z^3)) (32 E^(z/2) (3142699560 - 1702295595 z + 565134570 z^2 - 139958280 z^3 + 27941760 z^4 - 4696272 z^5 + 683424 z^6 - 87744 z^7 + 9984 z^8 - 768 z^9 + 512 z^10) BesselI[0, z/2]) + (1/(654885 z^4)) (32 E^(z/2) (-12570798240 + 6809182380 z - 2653375725 z^2 + 772701930 z^3 - 178378200 z^4 + 34086528 z^5 - 5561136 z^6 + 792480 z^7 - 100416 z^8 + 11520 z^9 - 1280 z^10 + 512 z^11) 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]