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

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=9/2, a₂>=9/2

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

For fixed z and a₁=9/2, a₂=11/2, b₁=-3/2

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(3/2), 4}, z] == (1/(99225 z)) (4 E^(z/2) (2835 + 24570 z - 113400 z^2 + 776160 z^3 + 3623760 z^4 + 3707424 z^5 + 1460928 z^6 + 253440 z^7 + 19200 z^8 + 512 z^9) BesselI[0, z/2]) + (1/(99225 z^2)) (4 E^(z/2) (-11340 + 945 z - 5670 z^2 + 32760 z^3 - 131040 z^4 + 1484784 z^5 + 2573088 z^6 + 1234752 z^7 + 235008 z^8 + 18688 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]