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

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.amlj.01

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(11/2), 3}, z] == (1/114604875) (4 E^(z/2) (33212025 - 47968200 z + 42543900 z^2 - 34171200 z^3 + 30693600 z^4 - 38868480 z^5 + 127491840 z^6 + 351959040 z^7 + 197879040 z^8 + 44820480 z^9 + 4727808 z^10 + 229376 z^11 + 4096 z^12) BesselI[0, z/2]) + (1/(114604875 z)) (4 E^(z/2) (-18243225 - 6081075 z + 24929100 z^2 - 25307100 z^3 + 20412000 z^4 - 17045280 z^5 + 17821440 z^6 - 30585600 z^7 + 208823040 z^8 + 159494400 z^9 + 40424448 z^10 + 4504576 z^11 + 225280 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]