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

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=11/2, a₂>=11/2

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

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

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(11/2), 5/2}, z] == (1/49116375) (49116375 - 117879300 z + 170270100 z^2 - 216216000 z^3 + 300736800 z^4 - 586051200 z^5 + 3008396160 z^6 + 4687978680 z^7 + 2387662200 z^8 + 591761940 z^9 + 80941500 z^10 + 6373824 z^11 + 285632 z^12 + 6720 z^13 + 64 z^14) + (1/49116375) (2 E^z Sqrt[Pi] z^(13/2) (2316733650 + 2831563350 z + 1324929375 z^2 + 314686575 z^3 + 41996850 z^4 + 3256680 z^5 + 144480 z^6 + 3376 z^7 + 32 z^8) Erf[Sqrt[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]