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

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=-9/2

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(9/2), 3}, z] == -((1/93767625) (4 E^(z/2) (-24962175 + 53411400 z - 71612100 z^2 + 92080800 z^3 - 153770400 z^4 + 634314240 z^5 + 2157684480 z^6 + 1644503040 z^7 + 527904000 z^8 + 83712000 z^9 + 6816768 z^10 + 270336 z^11 + 4096 z^12) BesselI[0, z/2])) - (1/(93767625 z)) (4 E^(z/2) (6081075 + 5145525 z - 24664500 z^2 + 36684900 z^3 - 45360000 z^4 + 63231840 z^5 - 135717120 z^6 + 1100770560 z^7 + 1223735040 z^8 + 453638400 z^9 + 77288448 z^10 + 6552576 z^11 + 266240 z^12 + 4096 z^13) 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]