Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1035)

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=1, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=1, b₁=3

http://functions.wolfram.com/07.25.03.1035.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {3, 6}, z] == (4 (-8 + 15 z))/(39 z^2) + (1/(178741037475 z^3)) (128 E^(z/2) (2027025 + 1155404250 z - 2675673000 z^2 + 2201945760 z^3 - 859355280 z^4 + 177680160 z^5 - 20314560 z^6 + 1274880 z^7 - 40704 z^8 + 512 z^9) BesselI[0, z/2]) - (1/(178741037475 z^4)) (128 E^(z/2) (8108100 + 38513475 z + 182432250 z^2 - 1359774360 z^3 + 1557168480 z^4 - 708629040 z^5 + 159159840 z^6 - 19099200 z^7 + 1234944 z^8 - 40192 z^9 + 512 z^10) 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]