Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0645)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=5

http://functions.wolfram.com/07.22.03.0645.01

Input Form

HypergeometricPFQ[{-(11/2)}, {5, 5}, z] == (512 (Sqrt[z] (40835452407750 + 99367856089425 z + 89389695641400 z^2 + 168764822503200 z^3 - 86485684824000 z^4 + 9292354513920 z^5 - 349011735552 z^6 + 5300404224 z^7 - 32555008 z^8 + 65536 z^9) BesselI[0, Sqrt[z]]^2 - (81670904815500 + 159264618645825 z + 131603406858000 z^2 + 116637159038400 z^3 - 80055657158400 z^4 + 9039218826240 z^5 - 345090705408 z^6 + 5276098560 z^7 - 32505856 z^8 + 65536 z^9) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] - Sqrt[z] (99359913269925 + 155605147461225 z + 129733957168200 z^2 + 131550454728000 z^3 - 82085783284800 z^4 + 9121725139968 z^5 - 346385746944 z^6 + 5284175872 z^7 - 32522240 z^8 + 65536 z^9) BesselI[1, Sqrt[z]]^2))/(47630017961150625 z^(7/2))

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]