Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1514)

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=5/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.1514.01

Input Form

HypergeometricPFQ[{-(11/2), 5/2}, {-(5/2), 5}, z] == -((1/(218243025 z^2)) (32 E^(z/2) (-31216185 - 7203735 z - 4698540 z^2 - 3090780 z^3 - 2836560 z^4 - 6769152 z^5 + 13375488 z^6 - 3596288 z^7 + 229376 z^8) BesselI[0, z/2])) + (1/(218243025 z^3)) (32 E^(z/2) (-124864740 - 28814940 z + 4584195 z^2 + 3104640 z^3 + 1917780 z^4 + 1474992 z^5 + 1900032 z^6 + 10123264 z^7 - 3366912 z^8 + 229376 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]