Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1056)

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=5

http://functions.wolfram.com/07.25.03.1056.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {5, 6}, z] == (8 (-384 + 1824 z - 2584 z^2 + 1615 z^3))/(4199 z^4) + (1/(19244451701475 z^4)) (1024 E^(z/2) (13749310575 - 72020198250 z + 120339471420 z^2 - 91630738080 z^3 + 36791430480 z^4 - 8399815200 z^5 + 1131943680 z^6 - 90682368 z^7 + 4200192 z^8 - 102912 z^9 + 1024 z^10) BesselI[0, z/2]) - (1/(19244451701475 z^4)) (1024 E^(z/2) (654729075 - 22783502070 z + 65598237180 z^2 - 64655468640 z^3 + 29847903120 z^4 - 7392077280 z^5 + 1047260928 z^6 - 86633472 z^7 + 4098816 z^8 - 101888 z^9 + 1024 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]