Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anpk)

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=11/2, b₁>=-11/2

For fixed z and a₁=11/2, a₂=11/2, b₁=-1/2

http://functions.wolfram.com/07.25.03.anpk.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(1/2), 3}, z] == -((1/893025) (8 E^(z/2) (-112050 + 2305125 z + 22697280 z^2 + 46352880 z^3 + 37386720 z^4 + 14314320 z^5 + 2799360 z^6 + 282624 z^7 + 13824 z^8 + 256 z^9) BesselI[0, z/2])) - (1/(893025 z)) (4 E^(z/2) (3375 + 14850 z - 414990 z^2 + 10740960 z^3 + 47844720 z^4 + 53051040 z^5 + 23798880 z^6 + 5073408 z^7 + 538368 z^8 + 27136 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]