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

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=9/2, b₁>=-11/2

For fixed z and a₁=3/2, a₂=9/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{3/2, 9/2}, {-(11/2), 3}, z] == (1/1091475) (8 E^(z/2) (-623700 + 382725 z - 126000 z^2 + 25200 z^3 - 5040 z^5 + 13440 z^6 + 24576 z^7 + 5120 z^8 + 256 z^9) BesselI[0, z/2]) + (1/(1091475 z)) (4 E^(z/2) (6081075 - 4054050 z + 1660050 z^2 - 504000 z^3 + 126000 z^4 - 30240 z^5 + 10080 z^6 - 8448 z^7 + 39680 z^8 + 9728 z^9 + 512 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]