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

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=-7/2

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(7/2), 6}, z] == (1/(694575 z^3)) (32 E^(z/2) (-827026200 + 419594175 z - 132162030 z^2 + 31082940 z^3 - 5896800 z^4 + 962640 z^5 - 171360 z^6 + 154368 z^7 + 347136 z^8 + 157440 z^9 + 23040 z^10 + 1024 z^11) BesselI[0, z/2]) + (1/(694575 z^4)) (32 E^(z/2) (3308104800 - 1678376700 z + 632026395 z^2 - 176694210 z^3 + 38884860 z^4 - 7025760 z^5 + 1063440 z^6 - 123552 z^7 - 17664 z^8 + 221184 z^9 + 135936 z^10 + 22016 z^11 + 1024 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]