Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amx7)

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=11/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.amx7.01

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(9/2), 1}, z] == (1/93767625) (E^(z/2) (93767625 - 562605750 z + 1541361150 z^2 - 3395876400 z^3 + 8748583200 z^4 - 52179422400 z^5 - 248686200000 z^6 - 288341544960 z^7 - 148685725440 z^8 - 40462087680 z^9 - 6245890560 z^10 - 559656960 z^11 - 28545024 z^12 - 761856 z^13 - 8192 z^14) BesselI[0, z/2]) - (1/93767625) (2 E^(z/2) (-78586200 z + 294400575 z^2 - 670534200 z^3 + 1480096800 z^4 - 4577731200 z^5 + 49495834080 z^6 + 92666488320 z^7 + 58059348480 z^8 + 17487912960 z^9 + 2863415040 z^10 + 266115072 z^11 + 13897728 z^12 + 376832 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]