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

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=5/2, a₂>=5/2

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

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

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

Input Form

HypergeometricPFQ[{5/2, 5/2}, {-(11/2), 6}, z] == (1/(6237 z^3)) (32 E^(z/2) (1466593128 - 515053539 z + 128648520 z^2 - 23634072 z^3 + 3393936 z^4 - 391152 z^5 + 36288 z^6 - 2624 z^7 + 128 z^8) BesselI[0, z/2]) + (1/(6237 z^4)) (32 E^(z/2) (-5866372512 + 2060214156 z - 697918221 z^2 + 158918760 z^3 - 27747720 z^4 + 3848400 z^5 - 431760 z^6 + 39104 z^7 - 2752 z^8 + 128 z^9) 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]