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

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, a₂>=5

For fixed z and a₁=5, a₂=6, b₁>=-11/2

For fixed z and a₁=5, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5, 6}, {-(11/2), 1}, -z] == (1/119750400) (119750400 + 653184000 z + 1524096000 z^2 + 2709504000 z^3 + 4877107200 z^4 + 11705057280 z^5 + 71530905600 z^6 - 147293966025 z^7 + 97155854100 z^8 - 31291162560 z^9 + 5653782288 z^10 - 607140960 z^11 + 39293120 z^12 - 1492992 z^13 + 30464 z^14 - 256 z^15) + (1/239500800) ((Sqrt[Pi] (-238097035575 z^(13/2) + 370373166450 z^(15/2) - 221162029200 z^(17/2) + 67714668000 z^(19/2) - 11878874400 z^(21/2) + 1252155840 z^(23/2) - 80049408 z^(25/2) + 3016192 z^(27/2) - 61184 z^(29/2) + 512 z^(31/2)) Erfi[Sqrt[z]])/E^z)

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]