Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a7q1)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=3, b₁=6

http://functions.wolfram.com/07.25.03.a7q1.01

Input Form

HypergeometricPFQ[{-(5/2), 3}, {6, 6}, z] == (640 (32 - 120 z + 65 z^2))/(1001 z^5) - (1/(135270135 z^5)) (512 E^(z/2) (5405400 - 22972950 z + 19114665 z^2 - 2802720 z^3 - 288600 z^4 - 344480 z^5 + 137040 z^6 - 14336 z^7 + 448 z^8) BesselI[0, z/2]) + (1/(135270135 z^4)) (512 E^(z/2) (-9352065 + 15590895 z - 3297720 z^2 - 467000 z^3 - 227600 z^4 + 123376 z^5 - 13888 z^6 + 448 z^7) 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]