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

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=-3/2

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

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(3/2), 3}, z] == (1/33075) (4 E^(z/2) (8505 - 41040 z + 297720 z^2 + 1454400 z^3 + 1557360 z^4 + 642432 z^5 + 116544 z^6 + 9216 z^7 + 256 z^8) BesselI[0, z/2]) + (1/(33075 z)) (4 E^(z/2) (-945 - 1215 z + 11160 z^2 - 48600 z^3 + 576720 z^4 + 1064112 z^5 + 538944 z^6 + 107712 z^7 + 8960 z^8 + 256 z^9) 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]