Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4157)

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=2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=2, b₁=3

http://functions.wolfram.com/07.25.03.4157.01

Input Form

HypergeometricPFQ[{-(9/2), 2}, {3, 6}, z] == 160/(143 z^2) - (1/(6241750515 z^3)) (512 E^(z/2) (135135 + 14054040 z - 5675670 z^2 - 13786320 z^3 + 10676940 z^4 - 2832576 z^5 + 336496 z^6 - 18048 z^7 + 352 z^8) BesselI[0, z/2]) + (1/(6241750515 z^4)) (128 E^(z/2) (2162160 + 6621615 z + 18378360 z^2 - 38959680 z^3 - 25925520 z^4 + 33190944 z^5 - 10088384 z^6 + 1275904 z^7 - 70784 z^8 + 1408 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]