Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ano4)

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=11/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.ano4.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(9/2), 6}, z] == -((1/(56260575 z^3)) (32 E^(z/2) (-15713497800 + 7753370625 z - 2408105700 z^2 + 556623900 z^3 - 101493000 z^4 + 13880160 z^5 - 2453760 z^7 + 8501760 z^8 + 22252800 z^9 + 11142144 z^10 + 2073600 z^11 + 157696 z^12 + 4096 z^13) BesselI[0, z/2])) - (1/(56260575 z^4)) (32 E^(z/2) (62853991200 - 31013482500 z + 11596610025 z^2 - 3202699500 z^3 + 697920300 z^4 - 126395640 z^5 + 20412000 z^6 - 3732480 z^7 + 1555200 z^8 - 2127360 z^9 + 13780224 z^10 + 9292800 z^11 + 1922048 z^12 + 153600 z^13 + 4096 z^14) BesselI[1, z/2])

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]