Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1773)

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=3, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=3, b₁=4

http://functions.wolfram.com/07.25.03.1773.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {4, 4}, z] == 96/(1105 z^3) + (1/(12692554875 z^3)) (16 E^(z/2) (-68918850 + 34459425 z + 18618840 z^2 + 817716780 z^3 - 1160096400 z^4 + 565803720 z^5 - 124743360 z^6 + 13365024 z^7 - 670592 z^8 + 12480 z^9) BesselI[0, z/2]) - (1/(12692554875 z^2)) (8 E^(z/2) (183410145 + 201200040 z + 441441360 z^2 - 1492513200 z^3 + 918388800 z^4 - 224693568 z^5 + 25426304 z^6 - 1316224 z^7 + 24960 z^8) 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]