Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1353)

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=2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=2, b₁=1

http://functions.wolfram.com/07.25.03.1353.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {1, 6}, z] == (1/(916620705 z^3)) (32 E^(z/2) (-997920 - 1465695 z - 1247400 z^2 + 27941760 z^3 - 66361680 z^4 + 44345952 z^5 - 11997888 z^6 + 1482240 z^7 - 82560 z^8 + 1664 z^9) BesselI[0, z/2]) - (1/(916620705 z^4)) (128 E^(z/2) (-997920 - 1465695 z - 1278585 z^2 - 748440 z^3 + 436590 z^4 - 9042768 z^5 + 8584212 z^6 - 2658624 z^7 + 350544 z^8 - 20224 z^9 + 416 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]