Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ak0q)

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=3, a₂>=3

For fixed z and a₁=3, a₂=7/2, b₁>=-11/2

For fixed z and a₁=3, a₂=7/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.ak0q.01

Input Form

HypergeometricPFQ[{3, 7/2}, {-(11/2), -(9/2)}, -z] == (1/147349125) (147349125 - 62511750 z + 35721000 z^2 - 37422000 z^3 + 97297200 z^4 - 1362160800 z^5 - 61751289600 z^6 + 626642956800 z^7 - 1245698092800 z^8 + 979970019840 z^9 - 385075169280 z^10 + 84268707840 z^11 - 10814361600 z^12 + 824893440 z^13 - 36470784 z^14 + 856064 z^15 - 8192 z^16) + (1/147349125) ((2048 Sqrt[Pi] (92534400 z^(13/2) - 493516800 z^(15/2) + 787449600 z^(17/2) - 557020800 z^(19/2) + 206388000 z^(21/2) - 43606080 z^(23/2) + 5473440 z^(25/2) - 411480 z^(27/2) + 18015 z^(29/2) - 420 z^(31/2) + 4 z^(33/2)) 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]