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

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=11/2, a₂>=11/2

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

For fixed z and a₁=11/2, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(7/2), 3}, z] == (1/93767625) (4 E^(z/2) (24026625 - 78246000 z + 170610300 z^2 - 414817200 z^3 + 2297846880 z^4 + 10085160960 z^5 + 10483603200 z^6 + 4708869120 z^7 + 1078652160 z^8 + 133976064 z^9 + 9028608 z^10 + 307200 z^11 + 4096 z^12) BesselI[0, z/2]) + (1/(93767625 z)) (4 E^(z/2) (-2338875 - 4039875 z + 29087100 z^2 - 68777100 z^3 + 145288080 z^4 - 421575840 z^5 + 4274000640 z^6 + 7054076160 z^7 + 3806403840 z^8 + 957329664 z^9 + 125395968 z^10 + 8727552 z^11 + 303104 z^12 + 4096 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]