Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4136)

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=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=2, b₁=2

http://functions.wolfram.com/07.25.03.4136.01

Input Form

HypergeometricPFQ[{-(9/2), 2}, {2, 5}, z] == -((1/(11486475 z^2)) (32 E^(z/2) (-2835 - 6615 z - 370440 z^2 + 476280 z^3 - 197040 z^4 + 33936 z^5 - 2496 z^6 + 64 z^7) BesselI[0, z/2])) + (1/(11486475 z^3)) (32 E^(z/2) (-11340 - 26460 z - 46305 z^2 - 105840 z^3 + 323160 z^4 - 166656 z^5 + 31536 z^6 - 2432 z^7 + 64 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]