Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al9i)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.al9i.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(9/2), 1}, z] == (1/1488375) (E^(z/2) (1488375 - 5953500 z + 11377800 z^2 - 18257400 z^3 + 35494200 z^4 - 163860480 z^5 - 610767360 z^6 - 519160320 z^7 - 185230080 z^8 - 32424960 z^9 - 2893824 z^10 - 124928 z^11 - 2048 z^12) BesselI[0, z/2]) - (1/1488375) (4 E^(z/2) (-529200 z + 1289925 z^2 - 2079000 z^3 + 3432870 z^4 - 8285760 z^5 + 72959040 z^6 + 93703680 z^7 + 39196800 z^8 + 7428096 z^9 + 692992 z^10 + 30720 z^11 + 512 z^12) 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]