Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an7r)

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=5, b₁>=-11/2

For fixed z and a₁=5, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.an7r.01

Input Form

HypergeometricPFQ[{5, 5}, {-(11/2), 1}, z] == (1/11975040) (11975040 - 54432000 z + 108864000 z^2 - 169344000 z^3 + 270950400 z^4 - 585252864 z^5 + 3251404800 z^6 + 5705913375 z^7 + 3198811194 z^8 + 862001172 z^9 + 127075032 z^10 + 10711248 z^11 + 510944 z^12 + 12736 z^13 + 128 z^14) + (1/23950080) (E^z Sqrt[Pi] (10352045025 z^(13/2) + 13986763056 z^(15/2) + 7155129744 z^(17/2) + 1841531328 z^(19/2) + 264381024 z^(21/2) + 21921024 z^(23/2) + 1034496 z^(25/2) + 25600 z^(27/2) + 256 z^(29/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]