Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an0z)

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=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.an0z.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(11/2), -(3/2)}, -z] == (1/49116375) (49116375 - 160744500 z + 1375258500 z^2 + 13621608000 z^3 + 61297236000 z^4 + 277880803200 z^5 + 2765575612800 z^6 - 10802095718400 z^7 + 12373885036800 z^8 - 6736769625600 z^9 + 2056179686400 z^10 - 381077726400 z^11 + 44645462400 z^12 - 3354233760 z^13 + 160126080 z^14 - 4666624 z^15 + 75264 z^16 - 512 z^17) + (1/49116375) ((16 Sqrt[Pi] (-353828412000 z^(13/2) + 943542432000 z^(15/2) - 940073526000 z^(17/2) + 476100828000 z^(19/2) - 139246364250 z^(21/2) + 25118969400 z^(23/2) - 2890500795 z^(25/2) + 214503450 z^(27/2) - 10151400 z^(29/2) + 294000 z^(31/2) - 4720 z^(33/2) + 32 z^(35/2)) 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]