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

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=9/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(11/2), 2}, z] == (1/114604875) (E^(z/2) (114604875 - 260678250 z + 317312100 z^2 - 324475200 z^3 + 354564000 z^4 - 530510400 z^5 + 2018822400 z^6 + 6432168960 z^7 + 4518362880 z^8 + 1343424000 z^9 + 198712320 z^10 + 15196160 z^11 + 569344 z^12 + 8192 z^13) BesselI[0, z/2]) + (1/114604875) (E^(z/2) (-30405375 + 126847350 z - 174881700 z^2 + 180532800 z^3 - 184212000 z^4 + 227505600 z^5 - 449245440 z^6 + 3438074880 z^7 + 3431681280 z^8 + 1165862400 z^9 + 184345600 z^10 + 14639104 z^11 + 561152 z^12 + 8192 z^13) 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]