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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(11/2), -(9/2)}, z] == (1/442047375) (442047375 + 267907500 z + 208372500 z^2 + 285768000 z^3 + 943034400 z^4 + 16345929600 z^5 - 899026128000 z^6 - 11428121779200 z^7 - 28627819718400 z^8 - 28830023470080 z^9 - 14847894190080 z^10 - 4401732787200 z^11 - 801513699840 z^12 - 92768417280 z^13 - 6904759488 z^14 - 327015936 z^15 - 9461760 z^16 - 151552 z^17 - 1024 z^18) - (1/442047375) (32 E^z Sqrt[Pi] (94354243200 z^(13/2) + 613302580800 z^(15/2) + 1212729537600 z^(17/2) + 1085743234800 z^(19/2) + 523067554800 z^(21/2) + 148856694840 z^(23/2) + 26400429720 z^(25/2) + 3002138685 z^(27/2) + 220741290 z^(29/2) + 10364760 z^(31/2) + 298032 z^(33/2) + 4752 z^(35/2) + 32 z^(37/2)) 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]