Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2220)

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=9/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.2220.01

Input Form

HypergeometricPFQ[{-(11/2), 9/2}, {-(9/2), 6}, z] == -((1/(32081724675 z^3)) (32 E^(z/2) (-57616158600 + 20847952125 z - 4281076800 z^2 - 726485760 z^3 - 149022720 z^4 - 38707200 z^5 - 13762560 z^6 - 7864320 z^7 - 12582912 z^8 + 16777216 z^9) BesselI[0, z/2])) + (1/(32081724675 z^4)) (32 E^(z/2) (-230464634400 + 83391808500 z - 24326327025 z^2 + 3710266560 z^3 + 614718720 z^4 + 121927680 z^5 + 30105600 z^6 + 9830400 z^7 + 4718592 z^8 + 4194304 z^9 + 16777216 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]