Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ano0)

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=-9/2

http://functions.wolfram.com/07.25.03.ano0.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(9/2), 4}, z] == -((1/(281302875 z)) (4 E^(z/2) (-18243225 - 68805450 z + 147136500 z^2 - 187790400 z^3 + 231789600 z^4 - 375036480 z^5 + 1508855040 z^6 + 5024332800 z^7 + 3726846720 z^8 + 1164142080 z^9 + 179801088 z^10 + 14278656 z^11 + 552960 z^12 + 8192 z^13) BesselI[0, z/2])) - (1/(281302875 z^2)) (4 E^(z/2) (72972900 - 6081075 z + 27130950 z^2 - 73653300 z^3 + 98884800 z^4 - 116030880 z^5 + 156219840 z^6 - 326903040 z^7 + 2602782720 z^8 + 2793703680 z^9 + 1004164608 z^10 + 166327296 z^11 + 13737984 z^12 + 544768 z^13 + 8192 z^14) 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]